Throwback Fact: The Birthday Problem

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In 1939, mathematician Richard von Mises proposed a problem. The answer was so counter-intuitive to many people, including mathematicians across the globe, that it continues to be one of the most discussed math problems ever. It is very difficult for people to understand, not because the mathematics behind it are hard, but just because the answer is so different from what anyone would expect. That problem is stated as follows:

Suppose you are in a large room that random people generally enter. How many people must be in the room before the probability that some share a birthday becomes at least 50 percent?

Counting Systems: Ancient Babylon

One of the most fascinating parts of math, for me, is the history behind it. Math is one of those things that shows up in every time period, no matter what civilization was in power or what languages were spoken. As a miniseries, I'd like to share some ancient counting systems and facts about math at that time. First up is the math of the Ancient Babylonians.

The Region: Babylonia was name of the cultural region in the fertile crescent, stretching from the Persian Gulf to modern-day Baghdad and west to the Mediterranean Sea. Their history dates back as far as 4000 BCE with the Sumerians, though very little is known about the Sumerian culture.

The Babylonian civilization rose and fell for millenia, and their culture can be classified into several distinct periods. The mathematical records that have survived come from two different periods: the First Babylonian Dynasty period (1800s - 1500s BCE) and the Selucid period (400 - 0 BCE). Very few documents fall between those two periods. The main focus of researchers are documents from the First Babylonian Dynasty, but the second period is interesting because it overlaps with great mathematicians from Ancient Greece.

One particularly famous Babylonian was Hammurabi, the king of Babylon for much of the 18th century BCE. Hammurabi's Code is the oldest known form of constitution for a government, and the stone on which it is written is the longest surviving work from the Old Babylonian period.

The Numerals: The scholars of Babylonia used cuneiform numerals to write their numbers. They pressed the wedge-shaped end of a reed into soft clay, and hardened it into stone tablets. The numbers are written from left to right like modern Latin numerals, but that is where the similarities end.

Problem of the Week

Happy Tuesday from the Center of Math team! Our Problem of the Week is coming to you one day later than usual because we celebrated Memorial Day yesterday. Here's the problem, which we posted on our Facebook, Twitter, and Google+ accounts just a little while ago:

As usual, I've provided my solution to this geometry problem below...

3 Memorial Day Mathematicians

image: www.nj.com

For the Center of Math, along with our United States fanbase, today is a public holiday. Many Americans celebrate with a backyard barbeque, or a day at the beach, but it's important to remember what Memorial Day is really for!

Of course, we're celebrating here by honoring a few math-minded people who have served in the United States armed forces. While there are surely many mathematicians who have served their countries all around the world (Alan Turing comes to mind), here are three Americans that you may not have heard of...

Throwback Fact: The Origins of Pi

We've mentioned pi quite a few times on the blog (our pi day post in particular). However, we've never discussed the reasoning behind the symbol.

Pi, of course, has existed in approximations since the time of the Babylonians (who got to 28/8 = 3.125) and the Ancient Egyptians (who found (16/9)^2 = 3.1605 on the Rhind Papyrus). Approximations have become better and better over time, but it will never end. Pi is transcendental- it is irrational, and cannot be found as the result of an algebraic function. We can continue to calculate more and more digits, but the number of trailing digits is an uncountable infinity, and therefore we will never know exactly what pi is.

Problem of the Week

 Happy Monday from the Center of Math team! Here's our newest Problem of the Week, which we posted to our social media accounts just a little while ago:

Click to expand!

A geometry and trig problem! We haven't seen one of these in a while. There are several ways to solve this problem, and I'll show just one of them below...