## Archive for the ‘Thrilling Math’ Category

### Great Formulas: V Squared Over r

Thursday, June 14th, 2012

All physics classes cover the formula for acceleration when the motion is in a circle. In an example usually given, the formula lets us compute the tension in a string when a mass at the end of the string is being spun in a circle.
Although the textbooks do not make a fuss over the formula, its discovery by Isaac Newton in 1655 was a landmark in the history of science. Deriving the formula required a great deal of insight into the nature of motion, and it was the starting point for Newton’s work on gravity and the motion of planets.
In this post, I will derive the formula using only basic mathematics, something physics courses do not usually do.

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### Eratosthenes Measures the Earth

Friday, May 25th, 2012

When did humans first learn the size of the Earth? Or, for that matter, when did it become clear that the Earth was a sphere?

To those not attuned to science history, it may come as a surprise to learn that the Earth’s size and shape were settled 2,200 years ago, and by the same person. In what was one of the great intellectual feats of antiquity, the Greek Eratosthenes took the measure of the Earth using only simple tools and mathematics, together with his creative mind. This post recounts how Eratosthenes did it.

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