HighFour History of Mathematics Category C: Grades 9 – 10 Round 6 Monday, February 22, 2016 The use of calculator is not required. Answer #1 Explanation: Answer #2: Explanation: Answer #3 Explanation: Answer #4 Explanation: Answer #5 Explanation: 4 In East Asia, some buildings do not have a 4th floor. (Compare with the Western practice of some buildings not having a 13th floor because 13 is considered unlucky.) In Hong Kong, some high-­‐rise residential buildings omit all floor numbers with "4", e.g., 4, 14, 24, 34 and all 40–49 floors, in addition to not having a 13th floor. As a result, a building whose highest floor is number 50 may actually have only 35 physical floors. Rene Descartes According to legend, one day, Descartes noticed a fly crawling around on the ceiling. He watched the fly for a long time. He wanted to know how to tell someone else where the fly was. Finally, he realized that he could describe the position of the fly by its distance from the walls of the room. When he got out of bed, Descartes wrote down what he had discovered. Then he tried describing the positions of points, the same way he described the position of the fly. Descartes had invented the coordinate plane! In fact, the coordinate plane is sometimes called the Cartesian plane, in his honor. August Ferdinand Mobius Mobius is now most frequently remembered for his discovery of the one-­‐
sided surface called the Möbius strip, which is formed by taking a rectangular strip of paper and connecting its ends after giving it a half twist.
Aristotle Using mathematics as a model, Aristotle presumed that all such knowledge must be derived from what is already known. Thus, the process of reasoning by syllogism employs a formal definition of validity that permits the deduction of new truths from established principles. The goal is to provide an account of why things happen the way they do, based solely upon what we already know. logarithm In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication.
HighFour History of Mathematics Category C: Grades 9 – 10 Round 6 Monday, February 22, 2016 The use of calculator is not required. Answer #6 Explanation: Answer #7 Explanation: Answer #8 Explanation: Answer #9 Explanation: Answer #10 Explanation: 6 The first perfect number is 6 as, 6 = 1 + 2 + 3. The next perfect number is 28, as 28 = 1 + 2 + 4 + 7 + 14. The next perfect number is 496, followed by 8128, all of which were discovered by Euclid in the 4th century BC. Mersenne primes These primes are named after Marin Mersenne, a French friar, who studied them in the early 17th century. The first four Mersenne primes are 3, 7, 31, and 127. Bertrand Russell The Principia Mathematica is a three-­‐volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
Pythagorean triples The smallest Pythagorean triples is 3, 4, 5, as 3* + 4* = 5* . parallelepiped In geometry, a parallelepiped is a three-­‐dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square or as a cuboid to a rectangle.
HighFour History of Mathematics Category C: Grades 9 – 10 Round 6 Monday, February 22, 2016 The use of calculator is not required. Answer #11 Explanation: Answer #12 Explanation: Answer #13 Explanation: Answer #14 Explanation: Answer #15 Explanation: Feynman point The sequence of six nines is called "Feynman point" after physicist Richard Feynman, who has also been claimed to have stated this same idea in a lecture. It is not clear when, or even if, Feynman made such a statement, however; it is not mentioned in published biographies or in his autobiographies and unknown to his biographer, James Gleick. Vinculum Vinculum is Latin for “bond”, “fetter”, “chain” or “tie”, which is suggestive of some of the uses of the symbol, which is to indicate that an expression is to be considered together. 40 (forty) 40, when written in words as “forty” is the only number with letters in alphabetical order, while “one” is the only one with letters in reverse order. Bonaventura Cavalieri Cavalieri was largely responsible for introducing the use of logarithms as a computational tool in Italy through his book Directorium Generale Uranometricum (1632; “A General Directory of Uranometry”). 1/100 seconds In electronics, a jiffy is the period of an alternating current power cycle, which is 1/60 or 1/50 of a second in most main power supplies. HighFour History of Mathematics Category C: Grades 9 – 10 Round 6 Monday, February 22, 2016 The use of calculator is not required. Answer #16 Explanation: Answer #17 Explanation: Answer #18 Explanation: Answer #19 Explanation: Answer #20 Explanation: Emmy Noether Emmy Noether was a German Jewish mathematician known for her landmark contributions to abstract algebra and theoretical physics.
Lewis Carroll Lewis Carroll is known for his word plays, logic, and fantasy. To promote letter writing, Dodgson invented "The Wonderland Postage-­‐Stamp Case" in 1889. This was a cloth-­‐backed folder with twelve slots, two marked for inserting the most commonly used penny stamp, and one each for the other current denominations up to one shilling. Alan Turing Alan Mathison Turing was a pioneering British computer scientist, mathematician, logician, cryptanalyst and theoretical biologist. One of his famous quotes is “a computer would deserve to be called intelligent if it could deceive a human into believing that it was human”. Pi An extension due to S. Bottomley adds instead the phrase "and if the lectures were boring or tiring, then any odd thinking was on quartic equations again.” The seven bridges of Konigsberg The problem was to devise a walk through the city that would cross each bridge once and only once, with the provisos that: the islands could only be reached by the bridges and every bridge once accessed must be crossed to its other end. The starting and ending points of the walk need not be the same.