CTK Insights » Beautiful math

Nested radicals

admin — Mon, 02 Aug 2010 16:21:09 +0000

Elsewhere we proved that the sequence (1) is convergent to 2. With this in mind, it is possible and meaningful to shorten the description of this fact to Expressions like that serve an example of infinite nested radicals. They are realized in terms of limits, if those exist, and are understood as the shorthand [...]

Nested radicals is a post from: CTK Insights

Unbraiding Braids

admin — Mon, 26 Jul 2010 18:22:03 +0000

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 [...]

Unbraiding Braids is a post from: CTK Insights

Radical Simplification

admin — Mon, 19 Jul 2010 16:33:06 +0000

In a related post I have shown that Without resorting to this proof, I am going to show that Let and Then which gives us a third degree equation in : By direct verification is one of the roots of that equation. Factoring gives The second factor which is a quadratic polynomial is always positive [...]

Radical Simplification is a post from: CTK Insights