How To Draw An Aztec Sun For Kids

Mexicolore contributor Terrence Summerson

Some thoughts on the blueprint of the Aztec Sun Stone

We are hugely grateful to Terrence Summerson, a 67-year-onetime retired professional draughtsman, for this insightful, stimulating and thought-provoking study of just how, technically, the Mexica might accept gone well-nigh designing the famous Sunstone. Terry writes:-
'I have had a fascination for Aztec history and fine art, particularly for the Aztec Sun stone, for as long as I can recall. As an enthusiastic amateur I have long been fascinated by the complex design of the sunstone and have often wondered how the creative person(s) actually planned and constructed such a large scale sculpture.
I take no academic qualification in archeology or Latin American history and so cannot comment on the various elements in the design; however I have produced many complex structural designs in the course of my career and have used this feel to effort and theorise how the basic outline of the Sunstone was created.
In the grade of these investigations I accept found many interesting coincidences between dimensions inside the Sunstone and known Aztec dimensions which may help in the report of other Aztec artifacts.'

Pic 1: Aztec sun stone showing the concentric circle design

Picture 1: Aztec sun rock showing the concentric circle design (Click on image to enlarge)

The calendar aspects as well as the mythical history contained within the Sunstone heightened my admiration for the creative person or artists responsible for producing such an awe inspiring piece of sculpture from the very outset.
I was so taken by the Sunstone that I decided that I would similar to make a copy, then I downloaded a few photographs and also some drawings and began to draw the basic pattern features. It was and then that I discovered that the layout was more circuitous than I start imagined as in that location were lots of concentric circles subdivided into diverse segments that did not seem like shooting fish in a barrel to decipher and construct (See motion picture 1).

Movie 2: Aztec body measurements (Click on image to enlarge)

The Concentric circles
I firstly focused on the multiple concentric circles making upward the pattern. I had no idea at this time that there was information available on Aztec linear measurements and so I decided to find the smallest distance on the stone and made that a size of one unit of length. I assumed that all dimensions would exist whole numbers equally I thought at the time that the Aztecs worked in ratios and not fractions or decimal places.
I then scaled all subsequent distances, from a motion picture of the sun stone, relative to the smallest distance of 1 unit in order to make up one's mind the radii and diameters of the main concentric circles within the pattern.
The radii of the circles identified were every bit follows:-
22, 24, 48, 50, 58, lx, 61, 66, 68, 72, 74, 75, 88, 90, 92, 102, 104, and 105. I then compared the radius of 105 with the actual size of the sunstone which was usually stated as 6ft. (1829mm) radius which divided past 105 = 17.42.

Pic 3: List of Aztec linear measurements (Click on image to enlarge)

Aztec Measurement
I and then began to search for information on Aztec linear measurements I subsequently establish several articles giving details of various measurements associated with different parts of the body. I article, 'The Dimensions of Holiness' by John E. Clark, listed several Aztec dimensions which I have shown graphically in Pic 2 and in tabulated class in Movie 3.
I conclude that my one unit dimension was uniform to the one finger dimensions of the Aztecs and that other Aztec dimensions might be found in the blueprint.
I therefore looked further into the various circle dimensions and compared them with the Aztec dimensions shown above and the results are shown in tabulated form in Pic 4...

Pic 4: Circle dimensions in the Sunstone

Motion picture 4: Circle dimensions in the Sunstone (Click on image to enlarge)

Segments of the circles
I and then turned my attention to the various divisions of the concentric circles and how they could have been measured accurately.
Although it was possible by trial and error or past the use of a protractor (see later) to carve up the circles into their relative segments I looked at the possibility of being able to use other methods such as geometry or mathematics to construct them.
Test of the design indicated that there were ix separate divisions of the circle and these were:-
• twenty segments – The Day Glyphs
• 8 segments – big and small-scale sun rays
• 52 segments – turquoise design
• 104 segments – feather design
• 16 segments – Blood perforator design
• 32 segments - dots and blood perforator turquois pattern
• 96 segments – claret pattern
• 34 segments – fire snake design
• 208 segments – exterior edge border design (See Pic five).

Pic 5: Aztec sun stone showing the various segments in the design

Pic five: Aztec sun stone showing the diverse segments in the pattern (Click on image to overstate)

The viii, 16 and 32 segments could easily be constructed using geometry to first create an octagon and and then using a compass to further subdivide the bending the circle of bore of 176 is the best one to choice up the points of the sun rays (See Movie vi).
The 96 segments tin be constructed by firstly creating a hexagon and and so using a compass to farther subdivide the sixty degree segments into 96 segments. The circumvolve of diameter 150 seems to exist appropriate as it is the base for the blood drops (Run across Pic 7).
To divide the circle into 20 segments it could be achieved by constructing a pentagon and and then subdividing the 5 sides. The circle with diameters 96 seemed to be the near likely one to use especially as the inner circle of 48 diameter tin can be used every bit the centre of two circles used in the construction of the pentagon (Encounter Pic 8).
The 34 segments can be achieved past amalgam a 17 sided polygon and and so sub-dividing to become the 34 divisions (See Moving picture 9).
To divide the circumvolve into 52, 104 and 208 would crave a 13 sided polygon which could and then be subdivided to requite the required divisions. Although it is impossible to actually construct such a polygon there are several ways to produce 1 that is reasonably accurate (Meet Pic 10).

Pic 6: The 8, 16 and 32 segments can be constructed by creating an Octagon

Movie 6: The 8, 16 and 32 segments tin be constructed by creating an Octagon (Click on image to enlarge)

Culling ways to split up a circle
Every bit I looked for ways of dividing the circle into the diverse segments I noticed that ane of the concentric circles had circumferences that was a whole number, this being the circle with radius 105.
I assumed that the Aztecs were aware of Pi and wondered if they had used that noesis to decide circles that could exist used carve up the circle into various segments (See Pic xi).
The obvious circles with whole number circumferences would be those whose bore was divisible by 7 (assuming Pi=22/7). Notwithstanding there was only one such circle and that was the outer edge circle with diameter 210. This circle has a circumference of 660 and could be divided into several combinations. ie.
2x33, 3x220, 4x165, 5x132, 6x110, 10x66, 11x60, 15x44, 20x33 and 22x30
This circumference could be used to split up the circumvolve into 4,8, 16, and 32 segments too equally 20 segments if necessary.
There were some other circles that was well-nigh whole and they were the circles with radius sixty, (the base of the iv big sun ray) and the circle with radius 92 (the circle contained in the fire serpents pattern).

Pic 7: The 96 segments can be constructed by firstly creating a hexagon

Pic seven: The 96 segments can exist synthetic by firstly creating a hexagon (Click on prototype to enlarge)

The circle with radius 60 has a circumference of 377.14 if we assume Pi = 22/7 all the same a more accurate version of Pi really gives a circumference of 376.99 and 377 = 13x29. This would hateful that you could measure out around the circumference 29 fingers which would divide the circle into 13 segments. Farther sub- dividing these segments using a compass would give you segments of 26, 52, 104 and 208.
The circle with radius 92 has a circumference of 578.29 if we assume Pi = 22/vii withal similar the previous example if we utilize a more accurate value for Pi we get a circumference of 578.05 and 578 = 34x17. This would hateful that yous could measure around the circumference 34 fingers to give 17 segments or 17 fingers to give 34 segments.
The fact that nosotros accept two different values of Pi beingness used seems to indicate that, like us, they may have used Pi = 22/7 for normal use and a more than accurate version of Pi for more detailed piece of work.
As stated above many of the angles could have been produced by using a protractor and so I prepare about trying to determine a method or methods required to construct one.

Pic 8: 20 segments could be achieved by constructing a pentagon

Film 8: 20 segments could be accomplished past amalgam a pentagon (Click on paradigm to overstate)

Amalgam a protractor
The first problem I had was how to construct a protractor that could be used to set of all of the required angles.
A 360 degree protractor could exist created on a diameter of 1146 which gives a circumference of 3600 with each caste existence 10 spaces.
With a 360 degree protractor information technology is possible to sub-divide a circumvolve into many parts: two,3,four,5,6,8,10,12,xv,16,18,xx,24,30,32,36,xl,
45,48,60,64,72,90,96,120,128, and 180.
However this did not embrace all of the angles required and I thought that it would be logical to copy what was already in identify and being used every bit a calendar and to have a protractor with 260 divisions and also 1 with 360 divisions.

Pic 9: The 34 segments can be achieved by constructing a 17 sided polygon

Pic 9: The 34 segments tin can exist achieved by constructing a 17 sided polygon (Click on image to enlarge)

A 260 caste protractor could be created on a diameter of 662 which gives a circumference of 2080 with each degree being 8 spaces.
With a 260 degree protractor information technology is possible to sub-carve up a circle into several more than parts :-2,iv,5,10,13,20,26,52,65, and 130.
The 260 caste protractor would give a right angle of 65 degrees, the 20 twenty-four hours glyphs would each accept an bending of 13 degrees whilst the 52 turquois patterns would be 5 degrees each.
Unfortunately neither tin sub-dissever the circle into 17 or 34 segments.
I and so thought that it would be really proficient if you could combine both protractors into ane.
By multiplying 360x26 = 9360 which gives a circle of about 2980 dia. And if you halved this diameter to 1490 this would give a circumference of 4681.

Pic 10: To divide the circle into 52 and 208 would require a 13 sided polygon. Although impossible to construct a 13 sided polygon this method is fairly accurate

Pic 10: To split up the circumvolve into 52 and 208 would require a 13 sided polygon. Although impossible to construct a 13 sided polygon this method is fairly accurate (Click on prototype to overstate)

4681/ 260 = 18 and 4681/ 360 = 13. This means that on the 260 caste protractor one degree equals 18 spaces and on the 360 degree protractor one caste equals 13 spaces (See Pic 12).
However if this was based on fingers so this protractor would be 25.926 metres in bore and really besides large. As a draughtsman I am always working with scale rulers and and then I realized that what was needed was a scaled downwards protractor.
When I worked with royal sizes they were unremarkably stated as fractions of an inch to a human foot and and so I looked at similar scales in the Aztec dimensions:-
1 finger=1 hand spans gives a scale of 1/12th.
1 finger=1 elbow gives a scale of one/24th.
1 finger=i heart gives a scale of 1/48th.
1 finger=1 hands gives a calibration of 1/96th.

Pic 11: Circles with whole number diameters and circumferences (Click on epitome to overstate)

If nosotros use a calibration ruler to draw these sizes to scale it would mean that the one finger distance would need to be sub-divided. Equally it is only 17.4mm long the maximum practical sub-sectionalization would exist 12 which would give a altitude of 1.45mm .
The i/12th calibration rule appears to exist more useful when working with other Aztec dimensions (Come across Pic 13 on how to produce a 1/12th scale ruler).
Going back to the protractor if we dissever 25926mm past 12 = 2160.5mm which although still quite big would be a more practical size.

Prepare squares
Autonomously from the compass and the protractor the other useful tools for the draughtsman are the T square and the set square. Commonly the set squares incorporate a correct angled triangle with either two 45 caste angles or a sixty degree and 30 degree angle. These are evidently related to the 360 degree circle and related to the construction of hexagons and octagons.
An equivalent set square based on the 260 degree circle with a right bending of 65 degrees and ii angles of 13 degrees and 52 degrees would exist useful in the construction of pentagons and twenty sided polygons.

Pic 12: Combined 360 and 260 degree protractor

Picture show 12: Combined 360 and 260 caste protractor (Click on epitome to enlarge)

Right angled triangles
Many of the Aztecs measurements tin can exist combined to produce Pythagorean correct angled triangles (for example from Picture ii).
12, 16, 20 (1 naab, 1 xocpilla, 20 mapillol)
24, 32, 40 (1 omitl, 2 xocpilla, 1 tlacxitl)
72, 96, 120 (1 arrow/dart, 1 maitl, 3 tlacxitl)
These right angled triangles are traditionally used to produce ninety caste angles and equally such could have been used in the construction of the sun rock design.

Pic 13: Construction of a 1/12 scale ruler

Pic thirteen: Construction of a 1/12 scale ruler (Click on image to enlarge)

Comments
In theory the methods stated in a higher place could have been used to produce all of the required segments present in the lord's day rock design withal all of the higher up comments and observations are only speculation on how the sunstone could have been designed and are not based on any facts or actual measurements of the sunstone itself. The artist could easily take used many other methods to pattern the sunstone which I am not aware of but I promise that at to the lowest degree this newspaper might stimulate comment and further written report into such an important part of Aztec life.

Pic 14: Painting of the sunstone without the fire serpents in order to show the various sub-divisions of the design more clearly

Pic xiv: Painting of the sunstone without the fire serpents in order to show the various sub-divisions of the design more clearly (Click on prototype to overstate)

Picture sources:-
Illustrations by Terry Summerson with reference to:-
• Sunstone photographs – Mexicolore
• Sunstone drawing – Thomas Filsinger
• Aztec Dimensions – John East. Clark, Dimensions of Holiness
• Structure of the Pentagon (5 sides) – Y. Hirano
• Structure of Heptadecagon (17 sides) – Herbert William Richmond 1893
• Construction of Tridecagon (13 sides) – Wikipedia.