Highly composite numbers have more divisors that any smaller number prompting Brady to coin the term anti-prime. Properties of these numbers were explored by the great Indian mathematician Ramanujan.
The Euler-Mascheroni constant is approximately 0.577 and is one of these numbers that pops up in various mathematics and physics problems. Yet the number itself remains mysterious. It is not even known if it is rational or irrational.
Secret Santa is intended to be an anonymous, random gifting pool. But is is neither random nor anonymous in all cases. But Dr. Fry has a clever modification to resolve those deficiencies.
The Feigenbaum Constant is a mysterious, probably irrational number that derives from a simple yet versatile equation for predicting population growth but quickly devolves into a chaotic fractal leading to the Mandelbrot set.
Matt shares a few curious ways to represent numbers up to 11,111 but their is a problem. The representation for one number is unknown. That's like an unscratchable itch to a mathematician.
Why can't you make a flat projection of a sphere like the earth without deforming it. The answer is Gaussian curvature. Euclid came close though, as Hannah demonstrates, it's not terribly practical.
If you think you know all the kinds of real numbers (That's right. No complex unreals.) you may be in for a surprise, particularly since even mathematicians don't know what kind most numbers are.
Mathematicians speculate that most numbers can be expressed as the sum of three cubes. And that those numbers with one solution have an infinite number of solutions. But the numbers can get big very, very fast. Take the number 3 as an example.
While Arabic and Roman numerals were battling for dominance in the MIddle ages the Cistercian order of Benedictine monks devised a clever numeric notation even more useless than Roman numerals for doing practical mathematics.
In their never ending search for prime number mathematicians came up with witness numbers. But some witnesses are more reliable than others. And don't expect them to help you find the factors.
Matt Parker demonstrates the incredible persistence to William Shanks who calculated the reciprocals values of thousands of prime numbers for no particular reason.
If you chronically lose the game of Risk, understanding its mathematics should help you. Fortunately, the mathematics has already been worked out for you.
Cones are counter-intuitive. They make no sense and never will. So just do the math. Though the math is persnickety too. So just remember; martini glasses are dishonest.
In a sequel to Matt's video on Caboose numbers Matt explores an obscure function that Ramanujan played with. It appears to generate whole numbers from a combination of irrational constants..
Playing with prime factors James Grime presents two kinds of number sequences with surprising properties that raise a host of questions in Brady's mind..
