# Rashmi Sunder-Raj

Mathematical Artist
I wish to tie together as many ideas as I can manage into neatly presentable packages. I feel driven to find visual representations of ideas, likely in a misguided attempt to make sense of all things. However, whatever the motivation, some interesting results occasionally fall out, so I'm not going to complain about the time involved in such a quest...only about those who do.
Some Adventures of the Rhombus Worms
0:03:34
Created using AnimationPro, Graphic and LumaFusion on an iPad Pro
2019
This film takes a light-hearted look at some properties of hinged shapes that I have been calling “Rhombus Worms”.

Given an angle θ (here I am only exploring those angles which divide nicely into 2π), a rhombus worm consists of a chain of rhombi with angles (θ,π-θ), (2θ, π-2θ), (3θ,π-3θ),...,ending in either (π-θ,θ) or (π-θ/2,θ/2) depending on whether or not θ divides π. The rhombi are hinged so that all lie on one side of a very bendy spine. If we let n=2π/θ, we find that the crescent shape formed can be rotated to form a simple n-fold rhombus rosette. The properties of these rosettes and worms are heavily dependent on the value of n mod 4.

As you will see, they have wormed their way into quite a bit of my recent art.
Unravelling Pascal’s Triangle
00:03:21
2019
This video is an exploration of a possibly unusual representation of Pascal’s Triangle using a woven binary tree. It seeks to present a way of looking at the triangle by separating each of its entries into a sum of ones, each treated as a separate thread weaving its way through the triangle affecting its other entries. It appears that some properties of the Triangle, including its recursive nature, can be visualized in this way.