I had the pleasure of meeting
then Amine of our US of

at the University of Minnesota.

He was my professor for my buildings
methods class during my undergrad studies.

He was a great assistant professor of
architecture and I'm not just saying that

because I got an A in his class his
expertise is in building technology and

is a researcher fellow at the center for
world heritage cities.

He graduated with a merit award from
antonymous National University of Mexico.

And also holds a degree in conservation
and restoration of the built heritage from

the excellence program of
Carolina Foundation and the University of.

Day in nearest Spain.

Ben Amine is now registered architect in
Mexico where he has been recognized for

his research and restoration work on
sixteenth and seventeenth colonial and

indigenous buildings in the haka
Mexico his work in Masonry and

geometry and Syria Tama tree has
been published numerous times

he has lectured in academic
institutions in Mexico Spain and us.

Please welcome Benami a barrister via

you think you really think you
very much for this very kind.

Actually that's how they called
me in the universe to Minnesota.

Ben how mean.

Because my name is Benjamin but
in Spanish is pronounced been her mean.

So it's quite familiar to
me through to her that.

They need to hear about
my name that way so

I really appreciate the opportunity
to present my work here.

The cultural park that you're
at the Georgia pick is quite

sure they are excited about it all
you want to thank all of you for

being here and
taking a little bit of your police and.

This lecture.

I also want to think Professor.

Down there right or for their invitation
it's quite an opportunity for

me as I mentioned before.

So I'm going to explain briefly but
in the next forty five minutes or

an hour a word that I have been developing
is a research work and this focused on

a story out of me is that we focus
on the geometry is focused on these

three things sent three
buildings in Mexico aim.

They have their work that
I have been developing is

to find these intricacies in
the construction of these buildings.

I feel this is a natural
source of inspiration for

a younger professionals
who are really driven by

their take in the technology the new
technology the digital work and

how we can combine the big question is
how we can combine a history and digital

technology how can we use contemporary
tools in order to understand our past and

have a clear understanding of our
present and hopefully our future.

So please a research project has been done

mostly thanks to
the A University of Minnesota.

I have had collaborators in Mexico as well

and I have had some funding from

the university grant in aid of research
our history and its color to program.

A matching form for
the Arts the humanities and design and

they were obviously they call it of
the scientists School of Architecture.

The content of this lecture
is pretty much what I want to

do first is to give you an introduction to
the buildings to show you there for you.

So know me their context
their relevance in the air.

In the in the in the historic
A environment in in Mexico and

I believe the entire Americas
then I want to show you this

how I tried to combine sixteenth
century treatises manuscripts and

combine them with cutting edge technology
for building construction analyses and

I want to show you some of my results and

conclusions I was commenting with
Tristen that I still have work to do but

so far I have gotten some interesting
results I believe that will be.

The illustrative of
these type of buildings.

The question here is why
these buildings in Mexico.

Right.
Why makes it go.

I well first of all because these
buildings haven't been really a study.

Right.

I mean there has been a lot of studies
in the context of sixteen got it later.

Gothic architecture be in Europe but

these buildings in Mexico
haven't been really addressed.

On the other hand something that I find
fascinating is that these buildings and

I want you to keep in mind as we move
through the lecture to keep in mind that

these building were actually built
by indigenous Native Americans of

the region this region is called
staker one is located in the state

of one Hark at the state of Ohio as this
hour in part in the territory of Mexico.

And this area where
the triangle the sand and some.

In some other areas around that.

Let me grab my pointer.

It's a it's called Steak and

it's an interesting area because
say it was highly populated during

the sixteenth century the Spanish
are ripe with this location.

And they develop into a monumental
buildings monumental Manas.

There is something that we
have to keep in mind and

take into account is something I also that
I always remind to my Spanish colleagues

when I talk to them if there are actually
these buildings were built from scratch.

Generally speaking in the in the European
context those buildings are actually

a this type of wheels are actually
embedded in the organ fabric.

But in this case they actually were
built in the middle of nowhere.

Usually they the town the post classic

settlements of the pre-Columbian towns
where up in the hills and when this

planet arrive they decided to bring all
the population down to the valleys and

change the transform
the production systems.

So the first one is about the star

is that is the Spanish name
is the indigenous name.

And that's how all the these towns
around this area are our name and aim.

If a moment a monumental
monastery with its church

its proper a monastery as you
can see on the plan right.

A large church at a smaller
building called the open chapel.

They opened chapel was a building that
would serve mostly for temporary.

Was a temporary building that
served mostly a a to host

large communities of people and
celebrate their new Christian ceremony.

So this is a typical more nasty

complex in sample from
following the principles and

the the same type of a continuation
that you can find in Europe as well.

These buildings were is important to
remember also that actually were built

between fifteen thirty five and
fifteen A.D. fifteen seventy five.

So as parties arrive to two that may.

Territory forty nine five three

did the Dominicans who were in
charge of these of this world

promoting this type of monastery
got there by fifteen thirty five.

It was a knife suitable type
of excuse scheme architectonic

a scheme that they will use for
a these type of of buildings

the next one is Santo Domingo
jam with woodland this is

a current photograph where I was is this
is the state of the of the of the of

the Church of the monastery the Corinth
the if you go to visit it tomorrow.

That's how you are going to find it which
pretty much shows that what you see there.

Now this is pretty close to what it
was during the sixteenth century where

the community the developed there was a
huge a pyramid by the end of the sixteenth

century that pretty much finished with
them higher population of the Mixteca you

benefit very few people survive and
never picked up again and

that's how you find an hour but they're
building is of monumental scale as well.

We see again the same configuration of
a single Naved church and a monastery.

So my vision is to the original
monastery in the lower part and

naturally I'm something that is
consistent in all the sixteenth century

a system centering one has
to consent of of Mexico.

This is the area where most of
the indigenous people will gather

before they will enter to the church or

accept to have to be brought into
the church for a religious ceremony.

This is the same the church right
we see again rape both storming

the roof the ceiling and this is
the plan again is a single naif bill.

With With this configuration
of balls in a square plan.

And the last building that I
a morning show you here was part

of the story Sampiero and the post call it

in this case is there not in chapel an
open chapel that was built with them and

money mentality with the scale
with the quality of construction

that you can find also in
the large churches as are X.

as I explained before
they open chapel will be.

Generally temporary structure but
in this case there was

the monumental structure of
the AME the configuration

of this is space is is similar but
is that the same time is different.

Right.
We have a centralized space right with our

vault on the center and

the people the original people will
gather over here in the normal room

to to celebrate the indigenous and we will
have to remember the Christian ceremony.

We have to remember that Indigenous
people were used to have their

ceremonies on the open
sky the the pre-Columbian

settlement show that their religious
ceremonies happened there.

Their cause more vision the way
they understand their religion was

connecting with the sun
the moon the stars etc.

So there was a transition in
the sixteenth century and

they opened chapel became
a popular model and

actually there were a lot of
experimentations happening in this

in this in this type of buildings
the churches and the monasteries

were there was some sort of code brought
from Spain right trying to control them.

Be sure of this pioneers who arrived
to do a news painter arrived to Mexico.

But the open chapel wasn't really part of
that core they didn't even know that that

existed so there were several
architectural experimentations and

beef is the most monumental and
the largest and the and the most complex

a open chapel that you can find
in the Mexican territory and

is unique because it
also hosts example null

vote but it hasn't been found
in any other places a grip

world has seen before in other places
around the globe in specially in Europe.

So these are the summary
the three different a monastery.

When I stick it in samples and
these are the three buildings

in which I am focusing on and
I'm pretty much focusing on the world.

Right which is which are they.

And they architectural feature of
these say of these buildings which

by the time were the cutting
edge technology right.

So I always tell my students that
if you see they opened chapel right

in the context of the sixteenth century it
was designed by Rem Koolhaas right who was

using the the cutting edge type
of technology of the time and

I'm going to show you why.

And I'm going to show you what
also how how that have happened.

But it's choir is what interest.

So all of these say type of

buildings are they from Italy
rooted in the in the Catholic

tradition the lead gothic that is
called in lead Catholic in in mostly

in the Iberian Peninsula is rooted
in this type of faith tradition

these are the documents of Lars of
one accord thirteenth century ride a.

Drawings by a actually
show how to build and

how to construct an arch for
instance over here.

A There was a measuring device.

So you can measure how tall the tower
is without going all the way to the top

of the tower and the Troy a rope or
something that just a forty

five degree strangle our very
simple a principle right.

Our falls arch over here right.

You can remove this central piece central
fake column analysts and you have

an arch without a column trying to trick
the people who seeing the structure.

Different types this is thirteen center is
one of the oldest if not the oldest legacy

of a Mason reconstruction is special in

the context of cathedrals
balls arches itself.

Don't fit in one thousand nine hundred
sixty one be a little go ape in Congress.

John.
And I would have also Robert eighteen

hundred but who have developed these
the theories about how the construction

of the vault evolved from the Romantic
period to the Gothic the and how actually

became the system that they used for
there was one of the main reasons.

According to feature in Dr is that.

Well we have the barrel balled the common
bar of all that we know the romantic

variable that needed bury the walls.

Right.

It was very little room for openings.

Then in order to to make the structure
lighter This is transparent the largest on

the on the wall that will make the main
a structural work and therefore and

then the space in between with
a large type of membrane and

then developing in this growing wall there
will be more versatile more flexible for

different type of spaces but
there was a constructive way.

Each issue when you start working
with these growing balls right week.

Have to pretty much if the your
meter is two cylinders

intersecting each other and generally
the generally speaking those cylinders

don't have the same radios right
don't have the same development.

So there was a different
difference in the within

the pieces right on the corner and making
a corner piece will be quite difficult.

So fitting proposes that actually that is
fixed and that is solved with the rape

the rape is to cover this this portion
of the wall that was not strong and

of will bring give give form to
the to the to the wall itself

the geometry the world will serve some
sort of some sort of form work right for

the for the masonry construction and
then be a little bit.

Also the will of this is this a all the
same methods of analyzing this type of.

Is quite interesting to remark here
that they what fiction is proposing and

ambulate the group belittling look as
well is that they every this arch is

a semicircle right that I am on a larger
we will study with more detail later and

what we what they used to do is to use
the same Also are the same pieces.

For all their arches right.

And that's how these are they pointed
arches Also while their use is this arch

rotate the arch to the to the plain
where these arch is right and

A And that's and that's how these
point of arch will will exist.

With that that is the main reason to
do this just to have a fabrication

process that will be much more a a much
simpler than a carving the stone for

each one of the arches because
each arch is different so

by carrying all the pieces
with the same radios right.

You have a lot of people carrying
one single type of piece and

use it in this thing to believe for
all the arches within the vault.

And what is also interesting
here is how Robert Willis.

And I will show you some other examples
for instance from a law now that

we are now Albert a daughter right there.

The role of the over the line
work in the conception

of a of the vaults how
the thought of presentation or

of different types of balls implant
obviously all of those are in speculations

right that none of the perhaps
some of these school be billed.

But what is what is showing here is
that the line drawing was a relevant or

was a vehicle to transform a type of

a configurations into a special
type of structures that A can be

achieved through arches and
compressive compressive members

they work of course the caliper last years
here that actually track they were ISIS

the different type of churches and
they JNA ology tries to create a genealogy

of the development of the Gothic and

A what happens in the late
gothic in Spain right with these

bury a exuberant type of
a designs that actually

take place in Spain during a fifteen
sixteen even seventeen center E.

and somehow they are actually brought
to a two to Mexico and these are some

examples within the territory of a Spain
they have a law that is when the laws

are used to live in Spain right and
we will see how these same configuration

of the world is very similar to what
we have in John with land in Mexico.

The analogy is used to show you how
exuberant these forms became right.

Just from a simple arch ride will
go from corner to corner and

support structure to this type of.

A of A A of A where created
by this by the by the rapes.

So there must be a master the technique

a incredibly and
they create these beautiful spaces and for

instance they were ghost Cathedral which
has all these transparencies right.

So where where well this a come from.

Well.

Well there are a few manuscripts and
we start here with the proper

analysis right understanding the
manuscript of the sixteenth century and

a and see how they translate
in different ways a so

there was a strong tradition
of masonry construction we can

use our use show you they say
this is a different world.

Right.
So within that strong that

tradition this large tradition
tradition of masonry construction.

Some of the Master Builders decided
to A to record all their knowledge

in manuscripts in treatises and they show

a different ways to a to understand and

to conceive both in systems and our other
problems of construction with masonry.

But we are going to focus on
the ball things just to have

a reminder right what
are the components of a bolt

of our report we are going
to have their eye on a ride.

Going from corner to
corner the tears are on.

That is going to be a secondary that is
going to divide this area into three.

We will see sometimes the rich rave
that is going to go from former

arch which are embedded on the walls or
transversal arch that are actually span.

To the axis of the NE
right where I want to

have it does the charge
which is this a piece or

sequence of pieces where all the rapes
converge and obviously the Keystone and

the secondary keystones are also
called bosses probably will.

He'll be on time your own shows how with
the hand you can actually a proportion

of the same the these say these
rapes are a little killed and

they have a sixteenth century
master builder and so with this.

Finger you do the former arch rivals and

have to be that thick because
he's embedded in the wall right.

Then you have a little thicker arch
which are going to be at the ears or

arms then you have it.

I want the largest a little
bit thicker if possible.

Again the next one the RAM
the rich rip it will run

panther in Spanish and
transverse a large is called

to appear in this planet which needs to be
a little bit stronger like the thumb right

because is growing across
the span of the church it's.

Let's see.

Well we don't see very well but
I want to ask you to.

To get a little bit of imagination here.

What we have here is a sixteenth
century document by Aaron and

Reese between fifteen fifty eight fifteen
sixteen dated between fifty sixty even and

he shows Square right over here and
he shows they

are a line going through one of
the ribs for showing there is

these circles that you see over here are
the keystone the different keystones or

BOCES right a little semicircle over

here to show the the charge right and
what he's showing is that they

line drawings of those large drawings
that we saw from the Da Vinci and.

Dürer right that this a Mason
is just a line drawing

that actually gives the configuration
of the bald implant right.

And then what he does is a bare tickle
projection of each one of those

arches is not are an elevation per se the
way we understand the liberation of many

human there's another you got him sketch
up and say cut here or right and you see

everything in projection what he goes is
that he takes each one of the arches right

and rotates the art to the plane
where he's going to draw them right.

So they can see them in his true form and
image.

So it takes one arch rotated to
this play and then one other

arch rotated to this plane and through
the arch and all the same thing for these.

So what he's showing here is your
single line drawings a defining

the geometry of the arches
in this case a way they

retrieve that you can't really see here
but it's a line going in this region and

going this reaction is these
lines over here right.

And that's going to be quite
important to define They A the height

of these Keystone and
therefore the radios and

the shape of these are in which
the air around is going to be

embedded what we see that these drawings
are not precisely construction drawings.

But they are and
they are useful to understand the geometry

of the world because one is a little
bit better if you say alone so

the bundle data will say father
was a master builder as well and

he decides to actually say a pig
the process that he lives is

if this is the right process
to do to conceive our world.

So what we see here again is a projection
implant a horizontal bridge from pilot

to the horizon.

We see a virus in this case we see is
there is it realize the axis of the ribs

and then are at the thickness
of the rib then we don't see

BOCES right we see those simple
intersection between those pieces

we start to see a more to more refined
type of technology relying in the in

the in the in the master pool a hoop
illustration of the technology

right we can see one of these pieces
here taking out from the plan and

again we see in the middle arches

drawn in this projection and
again he's doing exactly the same thing.

Each one of the they are Jesus is just
taking it to this plane and then followed

it back to the who is to this plane a
projection and then he defines each one of

them individually over here where we start
to see here or you can really not as but

what happens here is that we see that the
the ribs section right which in the gut.

It was really always the same section for
all of them we mention that

in this case the section it
starts to get distorted right.

But it starts to get distorted
to absorb to be part of

the geometry of
the curvature of this wall.

Which also speaks about how a day.

Really a master of the technology
at that period of time and

they are understanding of
the implications of this.

Of these geometries in in the in
the space which is quite interesting.

So the construction drawing but

it helps to understand how
this is actually done.

Now how can we use the digital tools
in communication with this type

of a type of a lot of drawings that.

You're still so the very first thing
here that show you is a bad idea.

It is what is called a scanner
a laser scan laser scanner

a technology which helps
to a top pain what

is called a point cloud and some of you
might be familiar with this technology.

So this is pretty much digital model that

A is made out of is a surface
made out of points writes

a point which allows to
register with some detail but

with a good level of detail they
space the pieces within a D.

in this case these churches right.

So it's going to provide a lot of
information with some level of

precision that is going to allow us
to analyze and on the wrist and what.

What's the down the line geometry
what is its constructive solutions

etc etc So the first part of the work was

you saw the point cloud is very
nice period going through them and

the church their very first thing is
to isolate one of the vaults right.

We focused on one of the walls and then
say OK this is the one that I'm on and

allies is very similar to the other
walls I'm going to focus on those so

obviously the political will is one single
ball right on a four giant woodland and

picked only one.

So once a day.

The point is isolated from
the rest of the of the world about

the of the church in the within
the point cloud then is

translated into the Ryman environment and
this is called Point two for

Rhino which is quite useful to do
the analysis of this type of of buildings.

So this is the Bury first day the very
first part bring it to Rhino and

start working with the holes
in themselves right uses.

Reminder we know that everything was done
in the horizontal and vertical direction

so the idea is to follow the same process
and understand what actually happened

within the construction of the boat so
we start with called our work.

So we can have a point cloud image over
here is looks like a photograph but

it's actually the point and
we start to understand how they actually

define the a geometry of
the underlying geometry implant for

each one of the arches remember
that happening by the leader.

So in this case is quite simple.

Right.
We have galleys became the I want us.

Well there isn't much to do they are one
and they were from corner to corner.

So there is our own are the ribs that

are going to define the different
difference in the design.

So in this case we find the midpoint on
the opposite side which draw a line we

find a triangle and
that's going to define the years

around with it happens
within with all the ball.

And we have this ring in the very very
center so that's what we care here.

So we have now triangle
defined by the balls or

the keystone right over here which
is happens to be an equilateral

triangle within the the this square and

we find the points where they intersect
that I want the ring inside is stange and

to the triangles that
we use found here and

that how we define the geometry or

how they define the geometry of these
balls implant very similar to what degree

somebody will be a bit in this case with
somebody Asians right because the designer

hats on the sign intentions as well within
the context that he was moving with.

So this is the final solution.

When we plan.

This is a very interesting wall because
it has double double their peers

around right over here this one and this
one is was a common practice when you had

a rectangular world right so
the distance between the let's

imagine that instead of rectangle
square these are rectangular All right.

What you're going to
have is a larger world.

Therefore their distance from the keystone
to these are right is going to be longer.

So this area is going to be quite big.

So Fear Factor or
get another rig in between.

So we covered the space and we are we
are we are good with with this case is

a squared type of walled square
plan with double double the tears.

You see tears and
I also have plans with our work anyway.

So how do we find these right.

Ridge No problem straight
forward we draw a collateral

triangle right sixty degrees and
we find for

a one on one hand this point and
on the other hand we find the line

defining the stairs or on the Harvester's
there's around in the vault.

We do the same operation with a with each
one of the sides of the world and a.

That's going to define
both the position or

the for this for these ribs and
the position for these rapes.

Right.
The same triangle and

a continuation of the tears
around is going to be fine.

There's still there's only going to
define this inner ring happening

within the well this is straight
line something that we found at

the vault of balls in
the areas in the level which

means that perhaps this was influenced
by those type of faults and then.

We find a these say the bolt of it.

The post color which I mentioned to you
before is our unique type of the president

and there is no other one with
this exact one a shape and

aim and
they where is interesting here is that.

Well everything is connected to
the A geometry of the right.

So what we are going to have
a game that I want as well.

Are going to be going from
corner to corner from birth X.

to Burdick's right then is when I find
that there is a runs over here and

we are going to have a series of a warped

reverse within the ball which are very and

the illusion I very south from South
are in Spain very elaborated right and

the center of each one of these of
these ribs is going to be located at

the intersection of these of these
say tranquil we have another

sequence of triangles happening within
this more X. I want to develop here and

we have the same solution to find these
smaller our word arches over here.

Rapes.

So that's the logic and we have these
other ones which are kind of tricky and

they actually develop in a completely
different way they are all part of these

your matric and the.

Much more advanced type of solution
which is related to the to the to

the to the plane that you can
find between the connection of

these pieces this is in the space within
the geometry of the vault of a within

the the metric expression of the ball
of this fear in this case right.

What we see over here so
that this is the the default.

So we can see here that there is a clear
translation between what happens in

the plan and
therefore the consequences on the way.

In the elevation or
the better protection is what

the next step will be are corded to when
they'll be there and man who is right.

So what what we do here in this case is
to cut sections through a point cloud.

So this is what you get to see on the
Rhine environment right through the wood

through the say plug in a sequence of
point that they are going to define

the the geometry of of the of the bolt
itself of which one of the arches.

SO WHAT A I did here was to cut by art by

each one of they are just
going through the point.

So these are these things
the sequence of artist right.

Each one of them an order to define what
the geometry the on the line geometry in

the liberation will be and

there are interesting things happening
in this ball right in this case.

Aim.

This is called slow walk.

This is going slower what we see here is
that this inner ring within the vault.

Is completely flat the some
follow an arch form so

there is not a continuous arch from this
point to this point there is an arch from

this point to this point flat an arch
from this point to this point but

that's how the geometry harmonize
quite logical because if we wanted to

embed this circle with towards
within the geometry of

Morris physical surface you had to
do kind of like a cone conical type

of geometry with the rapes or
he will be quite complicated right so

you just car some sort of ceiling there
over here and the top is completely flat.

Therefore they sent there of this art

right at the center of this
art is located right here.

We don't see there is a line
where you do it right here and

then which are all these are and
they will reduce our individually.

Right.
Each one of them is sold individually so

following the same logic right.

The gears are ons
are the same thing right.

You have these as a center
right up to the two to the line

where all the centers are and then you
draw segments of your conference and

that's going to define the geometry
of this arch over here.

So that's what is going to happen and
what it what it shows in

the context of bolting is that these
world is actually very gothic right.

Remember you mention that they will they
will they will carve arches individually.

So that's what is happening here and

A is not a preconceived form that we will
see in the in the next couple of posts.

So this is what is happening here and

therefore following
the exactly same logic right.

We see the former arches and transversal
arches being a semicircle which is center

is found right at the center of
the a span a of the arch itself.

So this is a work.

Now John we plan a lot of more sections
because there are a lot more arches right.

So we can have but
we found here is that actually the vault.

A response to the geometry of the sphere.

What does that mean.

Well what that means is that imagine that
this is a sphere implant and this fear is

also the fine in elevation or in medical
projection here is just a mis feel.

And each one of these arches
is as a section where

tickles lies through this fear.

So therefore the center of this
art is they made a point right.

You have a line that was from this point
to this point they made a point is right

here right.

You have the imposed line over here and

then you have the finishing
of that there are serious.

So there's or so
each one of these arches is going to be

where the callous lies
on the on the pier and

we can see here with more detail that
is what is actually happening so

is very different to what the in
in regarding these arches and

the same thing happens with it
in the lower tiers around right.

We have a section on the sphere
from this point to this point

they made point is where they
are the center is going to be and

that's where it's going
to define this arch.

Now what happens with the former and
the and the transversal arches.

Well what is one has to happen here is
that they are going to use what is called

a lab well to the larger one which is the
same system that we were looking before

proposed by right where
you have this arch and

then rotate the arch to this
plane to this plane and

therefore you have two centers and
appointed arch.

So they are used in exactly the same
exactly the same arch for those so

now we have a hybrid bolt
here is kind of is very

is under the School of the Renaissance
because a preconceived four is

a sphere is there you know the importance
of the of the sphere in the Renaissance

bar is using this the solution right.

The solution that we find
commonly on the Gothic bolts.

They're both cola a lot of more sections
where we cover a lot more rips deal with

but in essence the Pascola
is somehow is quite simple.

Do we have the a barrel rapes

which are going to be a semicircle right
is where we half of us are confident.

That's where we see here so
that of that forms.

Which forms a dome.

So the entire geometry of a Each
one of the arches is going to

respond to that dome is very similar
to John Wheeler Santa sphere.

So what we see here is that
these arches is a section

where tickles lies on and
it's very cold surface.

It's important to remember that all
these surface that we are talking about

happens only at the Internet or
they introduces this line.

The at the at the lower age of
the art itself right so it's a is a is

a is a form and I want to show you
some drawings of how that looks like.

So these off the very well this is
that they think points of circles and

art are lines that actually happen within
the ball itself they were also ours and

there are the formations B two I mean
the difference equation in the position

between the ribs the they actually
the actual surface is is just

just is different but
the underlying geometry is based on this.

So why Well what we see here is is
this I realise geometry that I have

shown that has been obtain through
these different sections to the ball

on AIM and how they arrive superimposed or
on are imposed

to the to the to the point cloud in order
to bury fi that that actually happened.

So what we see here and
then we see the world in

the point cloud then we see John we
plan we responding to the geometries.

We see the Pascola again.

Responding to that geometry juncture.

So what we have the fine so far is.

With the on the line geometry of the vault
right now using this method that

is proposed by Ben will be there and
and Landry's we understand that.

Yes is they follow the same
precept the same principles.

Now the next step is the history ARTEMY.

Certainly is the science that is
studies the cut of solids right.

And there is the ultimate for

wood and there is history of them in
four four four masonry four stone.

And these are joined by a million
beautiful drawing by Dr in evidence

shows they say drawn by feeling
where the Lord in France right.

This is a piece of stereo
to me that is lost but

it shows the intricacies
of these say these

in these work necessary to
create structures of this type.

So this is the information obtained
from the point plan we can see

seriously formations This is our work and
that's another type of story that can be

done in terms of the conservation and
the structural performance and

also provides the information to
a understand what what the family

these buildings we long to according to
us is there are three different ways to

A A two in two place they've also
ours in the course of the world.

So I was the first one is the English
style is a beautiful drawings by Willis

why the fan bald is quite female are right
there was so ours are pretty much

perpendicular to the bisect race
between the two to the two arches.

So this is what happens in the post
call in Jan woodland is more like

the French style they call it right to
ceiling there is intersecting each other.

Remember we talk about that as there
is position the placement of these A or

there was a large sum.

Talking about the pieces
between the ribs and

in the case of a of the political allies
call there are no that's in Spanish.

Right which is pretty much following
the dome a dome configuration.

So going back to the to
the third to me right.

We see the section of the of the river
of pain from the point cloud

then the different sections
between the three walls.

Remember these joined by a tiny one that
actually shows that some of them for

instance are jammed with land the Pascola
follow the recommendation of rather than

your own going with is called

a school school of one they're using
the same section for all the ribs and

increasing the only on transparency so
we can't either live German tree.

We have the section of the ribs and
then we have here the moral

of the of the boat itself always trying to

verify that it fits within the say

suck right between within this
say this surface created by

the a by the a a point cloud.

So the creating all reaps
the different connections then

you see this a point cloud a portion where

many sections similar to the sections
that we saw within the walled

dried many sections happened to each
one of the pieces and perhaps this

is when I look a little bit clearer right
away see different sections in Jell-O.

lined these blue light red lined gray
line in order to the find the geometry

of the piece itself started
to understand this there.

For me which is very much.

The form of the piece that is
where all these grips connect.

So then start to see the pieces.

We Sizwe in a more three dimensional
view in order to understand right.

How they are actually carved and

perhaps the next step will be to do to
actually develop that carving process and.

These pieces are twice as they're
being of this of this of this

piece of furniture is just quite big.

And the complexity within this piece
is that is also going to talk about

different things especially in the context
of a of the history of construction.

This is one of the of the typical a gothic

solutions' see the piece the ceiling.

There is within the Keystone
bird tickle him in this case.

This case.

These are these the axis of this piece is

leaning towards the center of the arch
in which this is is a embedded.

So these two different types of solutions.

There are quite a different and belong to
perhaps different traditions but some.

A configurations of how
the individual arches.

Can be seen from the construction
point of view and at the same

time in this case for instance that does
the charge which is a quite interesting

piece in the case it is a beautiful
piece of Injun woodland quite complex.

Right.

Hosting all the all the pieces
within the a the the ribs and

a I will separately from

any more illustrated.

Way of understanding how the.

I mean as I mention this.

I work in progress but it is pretty
much showing how these things are but

at the end what we got here is right.

Our catalogue of pieces that were
developed within this three sixteenth

century churches in the Mixtec and region
of Mexico quite complex piece of a vault.

That we're actually as I mentioned
built by a they missed me the mix

takes the people of the region of of
that region of the car by by by their.

Going back to the art
of graphic creation and

start seeing the pieces
in a in a different way.

Right.

And they want a different more traditional
way which personally I kind of

need to see right because
the information that

that provides is quite
Also interesting and then.

Well some sort of conclusions that I'm
going to draw here that are not precisely.

There are I mean as some sort
of conclusions right for

instance in the case of a very
gothic bald ride each of

the arches drawn individually the central
reminds of all proposed by bandolier

are that we saw originally by
the in that a manuscript and

also they are similar to the the balls
built in the cloister of sanest

they went through which
are attributed to one they

are ballon we talk about
how how these pieces these.

Reaps follow the keys
recommendations right.

With the same section for all the rapes
in the case of John woodland ride is

Morris is a concert of
the School of the Level A A uses

the double pairs around in a square
plan ride on a it was very sort

of former arches at the Sinulog well today
when Alice I as I mentioned before which

is why proposed a breeze in the drawing
of fifteen sixty and they are.

Any female are to they've
all of us into a little

more from coming from them that you
see our region was very elaborated

rips it reminds to the vault drawn
by where they were killed and

then you're in these vault over
here with this war arches that or

graves that we see here and we see here
which are happening here and here right.

So there is clearly a clear influence but
they are quite a different light.

So they've also of the church

is a square plan similar to that
was proposed by the manuscripts.

Nevertheless it is ordered to keep in
mind that the manuscripts are dated after

the construction of these boards
is a word using Day What is

important here again is to contextualize
that if you start at moment and

understand that these walls were designed
using the latest design principles or

the latest technology and
where a sign of the avenue guard of the of

the time and the square was
a suitable moral model or a base for

single nature which is which are kind
as characteristic of Mexico and

the only right there is there is a
question about the role of the of the rich

really right if you if you'd really
defines the geometry of the ball in

the case of the Mexican balls
the Boston riot is not really

a important aim they falso proposition by

the Spanish police on how
you draw you find it.

Here's your own grave in the in this
punish world by drawing it's a semicircle

right from from corner to corner
fine in the middle point and

drawing a line from this corner
to that made point we found that

in the Mexican balls is everything happens
everything within the constraints of

the geometry of the world right there
very substantial difference and

in the context of a history it has been
an assumption that because the proxy.

Between these three buildings has been
a historic assumption because there are no

documents to prove it and people
have really tried to find who was at

the signing of these masterpieces but
there has been

an assumption that it was the same one
because they are so close to each other.

Well this is study shows that they
are substantially different and

therefore the proposition is that
they were actually designed by

three different master builders
in them just as a reminder of how

high tech this is this is the right.

We know a conventional concrete beam
will be one sixteen of the span

will station concrete beam
is one twenty second.

The average is one two
hundred thirty eight.

Bill this fascinating is
structures by a day and

Felix candela are within this range
right one hundred seven hundred

twenty of a ritual between this band and
the.

Debate within this plan and
then there of the structural member

rates this plan is one forty
one forty fifth's not a bad

lot smaller than the post tension beam
ride in John woodland we call it with

take a car into account resort
where is this discussion about

what's the role of the of the of the rapes
if they really work is structurally or

not they do and they don't.

Right.
But if we take into account.

Only the there was a large we
are talking about one hundred one to one

hundred a span radio right one sixty
it is a membrane just think about it.

This is a membrane of stone
just working compression

smaller piece of stone working
compression creating these very very.

Very efficient the structures which
I will say are quite a remarkable.

And in their case of the political left.

These are the numbers is the busiest one

we have to remember that the protocol
is supported by columns only

at the contrary to the churches
that have these very thick walls.

So the definitely the say
they say Master Builder hut.

Is some some have to make
sure that this was strong

enough to do to be able to do behavior
enough so that it would then move.

We have to remember also these these
buildings are within a system it's own so.

Quite interesting just to see the cult how
thin those membranes are how our fish and

they are as a structure and what we
can pick from from but in order to to

understand the way we design our the way
we make the structures the way we

we we look at the buildings that

we try to do to create the in order
to be more efficient and much more.

But we might provide
perspective meaningful.

So with this I will just finish and

they Orpen it up for questions so
you have any Thank you very much for

the eloquent.

Yeah.

Well is aim as I mentioned earlier.

The open chapel as a type and the building
was in a restricted by the Spanish codes.

So.

As I mentioned there were there were there
were there was room for experimentation.

There was room to do
different types of things.

There was a very clear.

Programatic need and there was a very
creative master builder behind it and

he and I were very he was he

did something that I wanted
was quite a unique unique.

If you look at the configuration of
the world itself right at the X. I want.

But has some some in the drawings the
underlying geometry within within the X.

I want you thought there was the start
of the ride which can be brought back to

the roots of Christianism in utero
some perhaps that was also another.

I mean I used to think that it was
someone who really really understood

the construction system really
understood the technology.

Found.

Very skillful labor and

say we want to do something very
unique but and it is a strong piece of

Renaissance architecture because it's
can see it with a very centralized form.

It is and
this fear in this very very center.

I mean there are many things there is
a very contemporary piece of architecture

and so it was an excellent.

And excellent design.

Besides that I don't I don't I don't
find too many theories possible.

Yeah.

Yeah yeah.

Well there are a few large buildings in
this region a specific way in this region.

So the largest building.

Connected to this culture is
a complex in a large complex in.

In the state of what I called Miller and
in Midland you'll find are very refined

carving stone carving on the was creating
this very intricate patterns and

the piece of stone must be like
thirty inches by one inch all put

together within the wall and
it was very very very refined and so

well that shows that there was
a tradition of carving stone.

When you were analyzed the section of
those was the sections of midline or

in the case of Montel
one because of me and

build the want of I was in really occupied
with I think fifteen Hornets are the end

of the fourteen hundred and and
you see that technology is very similar.

I mean you have a core with more and
rubble and

then two sides of in the walls right.

With with much more will current
pieces of stone of Masonry.

And the corners will be
done properly right.

Having a corner peace etc
because the senses nikka.

So they were elsewhere not
precisely something different or

now the transfer is the transfer of
technology happened on the boards

differently and there is no more trouble
I mean there is a God this is a common

question in what extent
the Native American

in the mix takes of this region
actually change the process etc.

There is not much room to do that.

I mean is this follows very precise rules.

If you don't carve Well one of
those pieces the entire arch

is going to collapse.

So the idea is that you have
to have the right form or

the right shape of the piece and
there is one way of the one with perhaps

a mortar production but
as I mention probably sixty

Barbara Lee fifty years
to build this this been

in Europe would have taken a hole
in the right so there was a larger.

Population that embraced the technology
and was forced to actually do it.

So that's true.

So that's probably probably
probably the difference here.

But in besides that it's very difficult
to see if they covered one way because

they needed it was it was were brought
from Europe the US The US had the skills

definitely otherwise it
will happen possible.

This year

are limited by QUESTION So
what is the reason

why you mean why they made
this open chapel there was

that what was a quite monumental so.

Well I think that you're answering
the question definitely there was a strong

tradition to have this open space and
there was some

there was knows there is not a clear
reason the document that historically why.

In this case the political learn.

If people decided to build an open
chapel of those dimensions.

I mean.

There was there was some sort of
competition between the populous

the the little towns just
like happened in Europe right

which then had enlarged the tallest.

The tallest and the most monumental.

Perhaps instigated by the monks by name.

There is not clear understanding
why they decided to put all their

force from the open chapel and
make this monumental piece.

It was successful in all the settlements
in all the little towns there was this

little chapel that was very
useful at the beginning right

when the priest arrived and
then they gather all the images that

said now this is a new religion etc
etc But as their religion was accepted

by the communities they started to
build their own little chapels and

their own little churches and
they are usually was

either abandoned or their configuration
is you have the open chapel and

then once they can the community is
strong enough they are the church and

use the open chapel as an where so
you can see all this was successful.

We marched across the entire territory.

While in the post-colonial I was so
monumental and they put all there for

them all the money and
all the work is not that clear.

But it is definitely something
that we think right it was

very good they did it because we have this
very interesting building over this place

with this

one here.

They're

here they're

there they're

they're there

they're here they're

not with us.

It's in their cup and they're exactly.

There is a I mean there is record
there is record of that in

the area of Mary where the Mayans
were bundled dearest manuscripts.

But I think it stayed there not her.

I think that how that happened.

The Master Builders brought from
from Europe the god there and

work with the indigenous people and

taught them is what is called
foreign German terms where this.

This is the practical geometry right to
Carver's there's a bridge I'm pretty sure

that they had many mistakes but
at the end they achieved this type of.

Yeah that's a very good point there.

At the mall one and
order one coming with him and.

But that language was and
the other at the other issue and

we know that there are there
are documents off of both of these.

I don't know the name in English but this.

My mural colored to convert the question
is a great thing in SAP what they can

reading in Mystic so they call the great
support they can if there wasn't a written

language of to this point they
current develop that written language.

So they speak it but they don't.

And so in some areas they
are trying to do to achieve that.

Yes yes or a yes.

Yeah.

Myself there.

Yes there.

Yes that's correct.

But that's correct.

Their abuse of the or the piece is

yes exactly.

Not exactly that really story out of me or
this process of practical.

Geometry gave birth to what is now
understood as descriptive geometry and

the way we understand.

So it's a consequence of the construction
rather than Is that how it happened but

their way around.

Exactly.
Yes I think

there

are yeah

well it's great but

I'm in by lanes here and
there as well in the couple and

rejoin in the balance of religion you find
grasp the meaning of all this I mean by

a world of this fourteen
fifteen sixteen converts.

I mean it's just is what is
parallel there are actually some

buildings they had reports and
they on their need Bill.

Because it was more modern or
much more to see the board.

Together in one one building.

It was quite interesting.