T T T=<em>N</em>

Occasionally he made a comment similar to Archimedes' "Eureka!" about a discovery, as he did when he wrong T T T=N. This is part of number theory, the field that Gauss called the Queen of Mathematics. A triangular number T is a number that you can get by adding up a string of consecutive whole numbers beginning with one. The number 6 is triangular because you can get it by adding 1 2 3, and 15 is triangular because you can get it by adding 1 2 3 4 5. The number 5,050, the sum of the first 100...

 Archimedes Discovers How to Measure Volume

Hieron asked Archimedes to discover, without damaging it, whether a certain crown or wreath was made of pure gold, or if the goldsmith had fraudulently alloyed it with some baser metal. While Archimedes was turning the problem over in his mind, he chanced to be in the bath house. There, as he was sitting in the bath, he noticed that the amount of water that was flowing over the top of it was equal in volume to that part of his body that was immersed. He saw at once a way of solving the proble...

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It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped...