Note that here the " power index" also gives the number of zeros. The most widely used powers by whole numbers, for users of the decimal system, are of course those of 10 So, if that number is represented by "x" we getĪnd in general (since there is nothing special about 2 and 3 which will not hold for other whole numbers) The same will hold if "2" is replaced by any number. Since the first term contributes three factors of 2 and the second term contributes two-together, 5 multiplications by 2. What are they, in this example? Try guessing, choices are limited. "No," he replied, "it is a very interesting number it is the smallest number expressible as the sum of two cubes in two different ways."Ĭubes are third powers. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. I remember once going to see him when he was ill at Putney. The famous Indian mathematician Ramanujan was sick in a hospital (tuberculosis, probably) when he was visited by his friend the mathematician G.H Hardy, who had earlier invited him to England.Many listeners however are distracted by the many details given, miss the difference and perform the above calculation. Ives?" The answer is of course just one, the person telling the riddle. Sacks- 7 2 = 49 (but they are not part of the count)Īs noted, this is slightly modified from the original riddle, which asks "how many were going to St. Kits, cats, man, wives-how many were coming from St. Can you guess c?Ī slight modification of an old riddle goes: In a right angles triangle, a = 12, b = 5. The Greek Pythagoras showed (about 500 BC) that if (a,b,c) are lengths of the sides of a right-angled triangle, with c the longest, then.Note the use of parentheses-they are not absolutely needed, but they help make clear what is raised to the second or 3rd power. Similarly, a square of side 16.3 has area (16.3) 2 and a cube of side 9.25 has volume (9.25) 3. ![]() The number in the superscript is known as an " exponent." The special names for "squared" and "cubed" come because a square of side 2 has area 2 2 and a cube of side 2 has volume 2 3. ![]() "Two to the 6th power" or simply "2 to the 6th"" "Two to the 5th power" or simply "2 to the 5th"" "Two to the 4th power" or simply "2 to the 4th"" Powers of a number are obtained by multiplying it by itself. If the properties of powers are familiar to you, you may quickly skim through the material below. The concept of logarithms arose from that of powers of numbers. (M-14) Powers of Numbers Raising a numbers to the power which is a positive whole number
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