## Archive for September, 2010

### The Basel Problem

Wednesday, September 29th, 2010

The history of mathematics has many instances where someone has posed a problem for the mathematical world at large to solve, and the problem was not resolved for decades, or even centuries. Often, new mathematics has been discovered in the process of working out a solution.
This post is the story of one such case, the so-called Basel Problem, first posed as a challenge to European mathematicians in 1644. It withstood all attempts to solve it until, in 1734, young Leonard Euler found the answer. As the reader will see, Euler’s solution is a work of astonishing ingenuity, even though the level of the mathematics does not go beyond Algebra I.

Read the rest of this entry »

### How Henry Cavendish Weighed the Earth

Tuesday, September 21st, 2010

Most readers will be familiar with Newton’s Law of Gravitation, which states that the attractive force between two masses is proportional to the product of the masses, and inversely proportional to the square of the distance.
We can only determine the proportionality constant G if we can measure the force between two known masses separated by a known distance. Even Newton had no ideas for doing this, and thought the measurement might be {}“beyond the skill of man”.

Read the rest of this entry »