CTK Insights

Three ropes have been fastened to a horizontal plunk, tangled a little as if one tried to make a braid and, lastly, loosely attached to an auxiliary plank to keep them braided. Down below there is a third plank. The task is to attach three additional ropes to the first ones at one end and [...]

I found a remarkable talk given by Robert Lang pointed to at the Math Frolic! blog. Dr. Robert J. Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. Among other achievementsm he is known for having proved the completeness of Huzita–Hatori axioms and developing paper [...]

Some results are made to be shared. Fabian Rothelius came up with a simple iterative process that generates parallelograms after parallelograms with all the vertices on just three ellipses. His explanation underscores the power of affine transforms. Start with a parallelogram ABCD and generate another parallelogram A’B’C’D’: Repeat starting with A’B’C’D’: And then go on: [...]

Wonderment at the identity -1 = 1 + 2 + 4 + 8 + … dwarfes the perennial question as to whether .9999… equals 1 or not. Still, it holds in exactly same sense as the limit of a convergent series. The sums of the successive powers of 2 converge in the 2-adic norm! Moreover, [...]

Art in sand. No mathematics, but so beautiful.