Math Files

An Euler spiral is a curve in which the curvature varies in direct proportion to its arc length. It is commonly used in railway and highway engineering to create smooth transitions between straight paths and curved sections of tracks or roads.

1 = 1! 2 = 2! 145 = 1! + 4! + 5! 40585 = 4! + 0! + 5! + 8! + 5!

on April 29, 1832, Évariste Galois was released from prison after serving a six-month sentence. His arrest stemmed from events on Bastille Day in 1831, when he led a protest wearing the uniform of the disbanded artillery and was heavily armed with pistols, a rifle, and a dagger. Authorities charged him with illegally wearing a military uniform, leading to his imprisonment. Despite these circumstances, Galois continued to develop his groundbreaking mathematical ideas while in custody. After release tragically, just weeks later, he was shot in a duel on May 30 and died the following day, at the age of 20.

What if a number’s happiness wasn’t poetic, but something defined by mathematics? A happy number is defined by a simple process. Take any positive integer, split it into digits, square each digit, add the squares, and repeat. If the sequence eventually reaches 1, the number is happy. If it falls into a repeating loop that never hits 1, it is unhappy. Example (happy): 13 → 1² + 3² = 10 → 1² + 0² = 1 So, 13 is happy. Example (unhappy): 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 The cycle repeats, so 4 is unhappy.

Step into Non-Euclidean Geometry, and the world no longer behaves as you expect. Lines bend, space curves, and everything you thought was certain begins to shift.

Differential & Integral Calculus

Interviewer: your resume says that you’re quick in math. What’s 19x67? Me: 69 Interviewer: that’s not even close Me: But it was quick

Stefan Bergman was born on 5 May 1895. Born in Poland, he went on to become an influential American mathematician whose work focused mainly on Complex Analysis. In 1922, while at the University of Berlin, he discovered a remarkable mathematical tool now known as the Bergman kernel, which remains important in the study of analytic functions. Bergman later spent many years teaching at Stanford University, where he influenced generations of mathematicians through both his research and teaching.

x% of y = y% of x. For example: 8% of 50 = 50% of 8 = 4.