Al Jabr = Algebra

The word algebra comes from kitab wa al jabr wa al muqabalah.  This means “The Book of Shifting and Balancing” and is Al-Khwarizmi’s work describing six types of quadratic equations and their solutions.  He systematically collected and solved these problems in an algebraic manner, shifting terms from one side to the other and balancing terms on the collected side.  (1)

Goodwill Hunting: The Real Story

The movie Goodwill Hunting (starring Matt Damon, Robin Williams, and Ben Affleck) is based on the real-life story of George Dantzig.  Dantzig was taking a class at Berkeley with Jerzy Neyman, when he arrived late one day.  There were two problems on the board, which Dantzig quickly wrote down, thinking that they were homework.  He went home and solved them, turning in the solutions a few days later.  It turned out that those problems were not homework but two famous unsolved statistics problems!

Hypatia: The First Lady of Mathematics

The first noted female mathematician is Hypatia, who was born close to 355 A.D.  She was a very independent woman, wearing the clothes of a scholar and driving her own chariot.  She is well known for her mathematical work and her teachings, all of which survived well because they are explained in ways that are easy to understand.  Her life ended tragically due to political turmoil, but her work lived on as Descartes, Newton, and Leibniz expanded it.

Finite Area and Infinite Perimeter

It is possible to have an object with the properties of finite area and infinite perimeter.  In this object, the sides enclose a finite region but the sides are made up of infinite pieces.

Check out the Koch snowflake.  It starts with an equilateral triangle.  Then, on the first iteration, each side is broken so that a smaller triangle can be put on.  Then, each side is broken again so that yet a smaller triangle can be put on.  This is done infinitely so that you get…

A Different Angle

We learn in school that the measures of the interior angles of a triangle add up to 180 degrees.  Did you know that triangles on surfaces other than planes can have different sums?  The interior angles of a triangle on a sphere add up to more than 180 degrees, and the interior angles of a triangle on a pseudosphere add up to less than 180 degrees.  Why would anyone care?  Well, a triangle on a plane is a good study when doing calculations on a local area on the ground, such as what surveyors do.  Triangles on a sphere (elliptical geometry) give part of the picture of what is happening on our big ball of a planet.  Triangles on a pseudosphere (hyperbolic geometry) give part of the picture of what is happening to particles traveling in space.  It’s all relative, m’dear!

You Could Be the Next Winner!

Are you interested in a chance to win a cool $1 million?  Well, you could try playing the lottery, but the probability of you winning that is best saved for a whole other post.  Another way that you could take a shot at winning is by solving one of the seven Millennium Prize Problems.  The list and prize are the brain child of folks at the Clay Mathematics Institute of Cambridge, Massachusetts.

Actually, one of the problems has been solved.  Dr. Grigori Perelman is the winner of the $1 million dollar prize for solving the Poincare Conjecture.  Six other prizes are still up for grabs, though.  Just solve one of the following:

1. The Birch and Swinnerton-Dyer Conjecture

2. The Hodge Conjecture

3. Existence and Smoothness of the Navier–Stokes Equation

4. The P versus NP Problem

5. The Riemann Hypothesis

6. Quantum Yang–Mills Theory.

Good luck!

111111111×111111111

Why do so many people enjoy mathematics?  Is it because they like talking in some other language and sounding like an alien?  No, it’s because they like to solve puzzles and discover patterns.  Here is one fun pattern to ponder for today.

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

I encourage you to play with these by hand and see just why the answers work the way they do.  Also, stare at the answers and see if you spot any more patterns.  Have fun!