Download H4 History of Mathematics R1 G6

HighFour History of Mathematics Category B: Grades 6 – 8 Round 1 Monday, September 19, 2016 The use of calculator is not required. Answer #1: Explanation: Prime Numbers A prime number is a whole number greater than 1, whose only two whole-­‐number factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. As we proceed in the set of natural numbers N = {1, 2, 3, ...}, the primes become less and less frequent in general. Answer #2:
Explanation: Pi (3.14)
Pi equals the circumference divided by the diameter of a circle. Pi (π), the 16th letter of the Greek alphabet, is used to represent the most widely known mathematical constant. By definition, pi is the ratio of the circumference of a circle to its diameter. Answer #3: Explanation: Answer #4: Explanation: Answer #5: Explanation: common ratio For a geometric sequence or geometric series, the common ratio is the ratio of a term to the previous term. This ratio is usually indicated by the variable r. Example: The geometric series 3, 6, 12, 24, 48, . . . has common ratio r = 2. 180(n-­‐2) Representing the number of sides of a polygon as n, the number of triangles formed is (n -­‐ 2). Since each triangle contains 180°, the sum of the interior angles of a polygon is 180(n -­‐ 2). Aryabhatta Aryabhata was an acclaimed mathematician-­‐astronomer. He was born in Kusumapura (present day Patna) in Bihar, India. His contribution to mathematics, science and astronomy is immense, and yet he has not been accorded the recognition in the world history of science. HighFour History of Mathematics Category B: Grades 6 – 8 Round 1 Monday, September 19, 2016 The use of calculator is not required. Answer #6: Explanation: Answer #7: Explanation: Answer #8: Explanation: Answer #9: Explanation: Answer #10: Explanation: Benjamin Banneker Benjamin Banneker was a free African American almanac author, surveyor, naturalist and farmer. Born in Baltimore County, Maryland, to a free African American woman and a former slave, Banneker had little formal education and was largely self-­‐taught. Napier's bones Napier’s bones are slips of ivory or other material divided into sections marked with digits, devised by John Napier and formerly used to facilitate multiplication and division. Father of geometry Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He gathered the work of all of the earlier mathematicians and created his landmark work, 'The Elements,' surely one of the most published books of all time. Georg Cantor A popular German mathematician, Georg Cantor is famous for discovering and building a hierarchy of infinite sets according to their cardinal numbers. He is also known for inventing the Cantor set, which is now, a fundamental theory in mathematics. Fermat’s Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's
conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than two. HighFour History of Mathematics Category B: Grades 6 – 8 Round 1 Monday, September 19, 2016 The use of calculator is not required. Answer #11: Explanation: Answer #12: Explanation: Answer #13: Explanation: Answer #14: Explanation: Answer #15: Explanation: Euler's number The number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits are: 2.7182818284590452353602874713527 (and more ...) It is often called Euler's number after Leonhard Euler. Infinity Infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1657. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical. Cylinder In its simplest form, a cylinder is the surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder. It is one of the most basic curvilinear geometric shapes. Quadratic Equations A quadratic equation is a second-­‐order polynomial equation in a single variable. Because it is a second-­‐order polynomial equation, the fundamental theorem of algebra guarantees that it has two solutions. These solutions may be both real, or both complex. A perfect number Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. HighFour History of Mathematics Category B: Grades 6 – 8 Round 1 Monday, September 19, 2016 The use of calculator is not required. Answer #16: Explanation: Answer #17: Explanation: Answer #18: Explanation: Answer #19: Explanation: Answer #20: Explanation: Aliquot sum In mathematics, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n. The aliquot sums of perfect, deficient, and abundant numbers are equal to, less than, and greater than the number itself respectively. Icosahedron In geometry, an icosahedron is a polyhedron with 20 faces. The name
comes from Greek εἴκοσι, meaning "twenty", and ἕδρα, meaning "seat".
The plural can be either "icosahedra" or "icosahedrons". The Physical infinity Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical. Pythagoras The discovery of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2. Priori probability A priori probability is a probability calculated by logically examining existing information. A priori probability can most easily be described as making a conclusion based upon deductive reasoning rather than research or calculation. The largest drawback to this method of defining probabilities is that it can only be applied to a finite set of events.