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Pythagorean Theorem proof

By | 2018-04-23T14:19:10+00:00 September 25th, 2017|Greeks, Math|

A right triangle. This is the proof of the Pythagorean Theorem supposedly written by Pythagoras about 500 BC: The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). A2 + B2 = C2. Try it yourself: if Side [...]

Roman numeral answers – Roman math

By | 2017-09-04T21:37:29+00:00 September 4th, 2017|Math, Romans|

Roman tax collector calculating someone's taxes on an abacus (Metz, ca. 225 AD) Did you figure it out? Poor Claudia died when she was 25 years old, seven months, and fourteen days. It's very likely that she died giving birth to a baby, though it could have been dysentery or cancer or another [...]

Roman numerals – Ancient Roman numbers

By | 2017-09-04T18:16:56+00:00 September 4th, 2017|Math, Romans, Science|

Claudia Pieris' tombstone (CIL VI.15543) She lived 117-138 AD. Now in Copenhagen, at the Ny Carlsberg Glyptotek. The Romans used several different systems for writing numbers. Sometimes they wrote numbers like this: I II III IV V and other times they used the Greek numbers. Roman people didn't always write numbers the same way, [...]

European science – the Enlightenment

By | 2017-08-07T21:37:41+00:00 August 7th, 2017|Math, Modern Europe, Physics, Science|

Gottfried Leibniz, a German mathematician By 1650 AD, Europeans understood Islamic algebra and trigonometry better. Then they combined that with the exciting invention of the telescope and microscope. Together, these two new things led to a lot more new scientific discoveries. The Wars of Religion also got a lot of people thinking about what they really believed. How could you know for sure? [...]

Medieval math in Europe

By | 2017-08-04T13:22:07+00:00 August 4th, 2017|Math, Medieval|

Math was a very exciting subject to be working on during the Middle Ages in Europe. Little by little, math experts in Europe were learning from Islamic math experts about what we call Arabic numbers (0,1,2,3,4,5,6,7,8,9) (though the numbers came originally from India). Leaning Tower of Pisa (built while Fibonacci was a child) The first of these experts was Adelard [...]

Tangents – trigonometry – math

By | 2018-04-11T09:30:18+00:00 July 29th, 2017|Math|

Tangents: This line is tangent to a circle. What is a tangent? A tangent, like a sine or a cosine, is a mathematical way of thinking about a kind of movement that happens in nature. A tangent is really just a rephrasing of the same information we already had for calculating the sine function. Lines and circles [...]

Sine waves – trigonometry – math

By | 2017-07-29T17:59:39+00:00 July 29th, 2017|Math|

Sine wave In order to save energy, many, many things in nature move in a kind of repeated pattern we call a sine wave: water waves, sound waves, light waves, electricity, radio waves, and microwaves, for instance. The waves move in one direction quickly, then slow down until they stop, and begin moving [...]

Trigonometry and triangles

By | 2017-07-29T17:52:34+00:00 July 29th, 2017|Math|

An infinite distance: stars in the sky Since the time of the Sumerians, about 3000 BC, scientists have studied the stars and the planets. They've tried to figure out the patterns in the movements of the planets. This was much harder because everybody thought that the stars and planets circled around the earth, and really they don't. About 140 BC, [...]

Cosine – Trigonometry – Math

By | 2017-07-29T17:48:21+00:00 July 29th, 2017|Math|

Right triangle and cosine A cosine, like a sine, is a mathematical way of thinking about a kind of movement that happens in nature. A cosine is really just a rephrasing of the same information we already had for calculating the sine function. One way to describe these changes is with the sine function. Choose [...]