Sangaku – Sacred Math – Solving in AutoCAD - Part 2

[#1]

Note: This article was written and published in a different language and is a translated version of the original published here.

The wooden plaques known as Sangaku (or San Gaku) were hung in Japanese Shinto temples and shrines presenting geometric, arithmetic and algebraic problems with the intention of stimulating and propagating mathematical knowledge among adults and children or as offerings to the gods to thank for the resolution of a mathematical theorem.

The figure shows a plaque from 1854, with various problems located at Sugawara Tenmangu temple – Mie prefecture.

My proposal is to fix the problem indicated in the figure in AutoCAD.

Problem 1:

Three squares of sides a, b, and c are inscribed on the equilateral triangle of side k.

On the square side c are inscribed two circles of radius R and r and an equilateral triangle of side d.

If a = 7.8179, find b, c, d, k, r, and r.

See figure in AutoCAD.

Solution:

Problem 2

The third Sangaku in the lower right corner and is part of the plaque presented at Katayamahiko temple in October 1873.

Draw in Autocad and solve the question:

The figure shows a square ABCD with side 1 and center O. Circles O1 and O2 are equal and are inscribed on the square and tangent to O.

EF and E1F1 are common tangents to O1 and O2. X-ray circle O3 is tangent to AB, BC, and FE.

X-ray circle O4 is tangent to the HA, CD, and E1F1.

What is the X-ray value?

Solution:

Problem 3:

This sangaku was created by  Tanabe Shigetoshi, fifteen years old in 1865 at Meiseirinji Temple in Ogaki City, Gifu Prefecture.

The point of the statement was to calculate the radius of the yellow circle in relation to the radius of the dashed circle.

Modifying the statement. Draw the figure in Autocad knowing the measurements:

Green circle radius 60

Red Circle Radius 20

Calculate the radius from the yellow circle and the total area indicated in blue.

Solution:

Sangakus were created to be solved through mathematical calculations.

But in Autocad there can be multiple solutions.

It depends on the reasoning of each one.

I tell my students:

What is easy for you may be difficult for me. An example is to draw a square, you can use the Rectangle, Polygon, Polyline command and even with the Line and Join command.

See you next time.

Hugs and stay well! 

Which is easier and more practical?

Will the result be a square? Ok, it's valid.

Hugs and be well!

problem 1.mp4