# Modeling Nature

You know those movies with all of the realistic scenery and special effects?  What you are seeing on the screen may or may not be real, and the effects are often made possible by applying fractal techniques. Fractals are the answer to creating irregular geometric shapes such as mountain ranges and coastlines.  That is because, […]

# The Big Reveal

Okay, the answer from yesterday’s post is… (DRUMROLL PLEASE) 5050 How did he get that?  Well, he did not start by adding 1 + 2 + 3 + …  Instead, he found a pattern. Try writing 1 to 100 on one line and then 100 to 1 on the next.  Add up the numbers directly […]

# Mental Sum

Take a moment and add up the numbers 1, 2, 3, …, 98, 99, 100.  Now, there’s a catch before you try.  Do it in your head, and you have 10 minutes. If you did it, congratulations!  Please don’t share the result, though.  If you did not do it, reflect on the fact that Carl […]

# Striking Goldbach

Goldbach’s Conjecture was first proposed in a weak form by Christian Goldbach in the 18th century and then in a stronger form by Leonhard Euler.  It says that every odd number can be broken up into a sum of, at most, 3 prime numbers. 35 = 19 + 13 + 3 21 = 3 + […]

# Sacrificial Solid

A dodecahedron is a solid, 3-D figure made up of 12 regular pentagons. It is said that when the dodecahedron was discovered, the Pythagoreans sacrificed 100 oxen in celebration.  (1)

# Mathematical Graffiti

Speaking of Sir William Rowan Hamilton and quaternions, the solution to how to multiply quaternions came to Hamilton one day while he was out on a walk with his wife.  Worried that he would forget, Hamilton immediately carved the answer in the Brougham Bridge.  That piece of mathematical graffiti went unpunished and in fact is […]

# When are we ever gonna use this?

Sometimes, mathematical discoveries come about because people are trying to solve real-world application problems.  Other times, mathematical discoveries come about because people have incredible imagination and insight, but then those discoveries are seemingly useless, for a while. Quaternions are something that fall into the latter category.  These members of a noncommutative divisional algebra were first […]