The 12-30 project, animated HD for the month of November “Current Sangaku” – is now on Vimeo. Images of the sequence were originated in Geogebra. Additional credits: Yutaka Yamada, Derek & Brandon Flechter for the music.
The 12-30 project https://jcdigitaljournal.wordpress.com/
The 12-30 project is going to Jyväskylä this August!
Left a 16-cell polytope, right a seven symmetry hyperbole. Original plates – the 12-30 project – 05-08, 05-26.
The project images are coming out of the box! The first one is going to Slovenia, the second in Taiwan and the third in Israel. The original work & text can be found on the 12-30 site, category 01-January. Respectively, January 8, January 17, January 19.
The 12-30 project https://jcdigitaljournal.wordpress.com/
December 5. – 339
MathMod & Morenaments. The flight of the owl. Variation on Maeder’s owl – A minimal surface found by Roman Maeder, author of the book Programming in Mathematica, the standard reference for programming
Background – a pmm symmetry.
The 12-30 project https://jcdigitaljournal.wordpress.com/
December 2. – 336
MathMod & Morenaments. Inspiration from mathematical objects comes in many shapes – Today, a floral pattern from a Henneberg parametric surface – a non-orientable minimal surface named after mathematician Lebrecht Henneberg.
I kept the original visualization – as is – in a reflection on the vase holding the flowers.
The 12-30 project https://jcdigitaljournal.wordpress.com/
December 1. – 335
MathMod & Morenaments – I started the year with SURFER from Imaginary.org. I might as well close the year with the Imaginary.org programming community.
MathMod is a mathematical modeling software. It visualizes and animates implicit and parametric surfaces. It was created by Abderrahman Taha and is available at SourceForge
Morenaments was created by Martin Von Gagen and is available on the Imaginary.org site. The program creates symmetrical patterns in one of the 17 symmetry groups of the Euclidean space.
The combination of the mathematical objects from MathMod and background patterns Ill create in Morenaments should make for an interesting visual dialog.
Today’s object is a cube-sphere – how to turn a cube into a sphere – which is done by connecting the mesh/vertices from one to the other. I slightly tweaked the script to make them overlap instead of just blending – still an all in one cube in a sphere. I used the Morenaments background to create the drop pattern around and in the spherecube.
The 12-30 project https://jcdigitaljournal.wordpress.com/
Geogebra. This sangaku is intriguing because of the symmetrical aspect of its geometry. It asks to find the diameter of the smallest circle(s) in terms of the central circle(s).
The 12-30 project https://jcdigitaljournal.wordpress.com/
Geogebra. If this image had been drawn on a flat 2D surface, we would find two equivalent squares, one tilted at 45º. The figure contains 2 circles in the inside surface where the squares overlap. Find the size of the lower circle in terms of the upper circle. Here squares are cubes and circles – spheres.
The 12-30 project https://jcdigitaljournal.wordpress.com/
November 19 – 323.
Geogebra. Sangaku problem from the Katayamahiko shrine. Four circles of radius r and four congruent equilateral triangles of side a touch a big circle of radius R internally and also touch a small square of the side a. Find r in terms of R.
Note that on the image, the circles have been transformed in spheres, the triangles into pyramids and the square in a cube.
The 12-30 project
https://jcdigitaljournal.wordpress.com/
October 31 – 304.
The Kuen kabuki. In mathematics, a Zoll surface, named after Otto Zoll, is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. The Kuen surface is a special case of Enneper’s negative curvature surfaces
Background: Hubble telescope. Galaxy Cluster MACS J0717, 5.4 billion light-years from Earth. It is one of the most complex galaxy clusters ever seen.
The 12-30 project 
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