How to easily solve a nested radical equation,,,
You can adapt it to any repeating basic math operator in the infinitely nested radicals. The above nested radicals can be equal to whatever you want except 1, this is due to the particular multiplicative identity properties of the digit 1 (for instance, √1 = 1 and 1² = 1).
The beautiful proof of why √2 ∉ Q
Complex knot equivalent to the unknot.
When the absurd of the absurd is real.
In fact, i√i = eπ/2 = 4.81…
This is a set of symbols developed for prime powers by the Italian mathematician Francesco Ghaligai in 1521. These were used where today we would use a named variable and a power.
Geometric shapes are not limited only to the figurative aspect, they can also play active roles, for instance, serving in microelectronics to build operational printed circuits such as: small inductors (magnified, fig. a below), resistors (fig. b) and capacitors (fig. c). (image taken from my book “Almanach du Mathématicien en Herbe“)
A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?
This puzzle is available as greeting cards from my online store.