HighFour History of Mathematics Category A: Grades 4 – 5 Round 6 Wednesday, February 15, 2016 The use of calculator is not required. Answer #1: Explanation: Answer #2: Explanation: Answer #3: Explanation: Answer #4: Explanation: Answer #5: Explanation: Fraction A fraction represents part of the whole or more generally, any number equal parts. The word fraction came from the Latin word “fractio” which means to break. Fractions were created by the ancient Egyptians in 1800 B.C. Quadrilateral Quadrilateral is a geometric shape that consists of four points (vertices) and four sides. Quadrilaterals can be either concave or convex which means that if you extend their lines they will be either go through the shape or not. In ancient times quadrilaterals were used for art, design, and architecture. Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz introduced ≅ for congruence in an unpublished manuscript of 1679. The first appearance in print of Leibniz' sign for congruence was in 1710 in the Miscellanea Berolinensia in the anonymous article “Monitum,” which is attributed to Leibniz. Leibniz is also often considered the most important logician between Aristotle in Ancient Greece and George Boole and Augustus De Morgan in the 19th Century. Percent (%) Percent came from the Latin phrase per centum which means the hundred or for every hundred. In the 17th century Europe, the symbol was often used as an abbreviation for percent. This ancient symbol has evolved into the % symbol, which is commonly used today. Roman Numerals Roman numerals are letters of the alphabet used in ancient Rome to represent numbers: I=1; V=5; X=10; L=50; C=100; D=500; M=1000. It is a system that uses addition and subtraction. HighFour History of Mathematics Category A: Grades 4 – 5 Round 6 Wednesday, February 15, 2016 The use of calculator is not required. Answer #6: Explanation: Answer #7: Explanation: Answer #8: Explanation: Answer #9: Explanation: Answer #10: Explanation: William Jones In 1706, a little-­‐known mathematics teacher named William Jones first used a symbol to represent the platonic concept of pi (𝜋). Thales of Miletus It was during the first half of the 6th century that Thales of Miletus computed the height of the Great Pyramid in Egypt by an ingenious method of indirect measurement. Historians claim that geometry began with him. He is given credit for having made a number of elementary discoveries. Arithmetic Arithmetic comes from the Greek word arithmos, meaning number. It is the oldest and most fundamental branch of mathematics. It is used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. Some have called it the "science of numbers." Decimal Decimal comes from the Latin word “decimus” meaning tenth, from the root word decem, or 10. It is a term that describes the base-­‐10 number system. It was invented by Hindu mathematicians in India between the 1st and 6th centuries A.D. This system is sometimes also called the Hindu-­‐
Arabic numeral system because it was first introduced to Europeans by Arabs, who had acquired the system from the Hindus earlier. Roman Numerals Roman numerals are letters of the alphabet used in ancient Rome to represent numbers: I=1; V=5; X=10; L=50; C=100; D=500; M=1000. It is a system that uses addition and subtraction. HighFour History of Mathematics Category A: Grades 4 – 5 Round 6 Wednesday, February 15, 2016 The use of calculator is not required. Answer #11: Explanation: Answer #12: Explanation: Answer #13: Explanation: Answer #14: Explanation: Answer #15: Explanation: Euclid of Alexandria Euclid of Alexandria is called the “Father of Geometry”. He received his education at Plato's Academy in Greece and moved to Egypt to teach. Euclid is famous for the mathematics textbooks “Elements," which contains lessons on algebra, number theories and geometry. Angles An angle is the union of two rays with a common endpoint called the vertex. The rays are the sides of the angle. The word angle comes from the Latin word angulus, meaning “a corner”. Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. Pierre de Fermat French mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Fermat discovered the fundamental principle of analytic geometry. Exponent/Index/Power The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number. Euclid discovered the concept of exponents, which he used in his geometric equations. Archimedes later generalized the idea of powers in his work, “The Sand Reckoner”. He discovered and proved the laws of exponents in the same work. René Descartes René Descartes is considered by many to be the father of modern philosophy, because his ideas departed widely from current understanding in the early 17th century. He invented the Cartesian plane in which the name Cartesian is derived from his own name. He is recognized as the inventor of analytic geometry, which is a way of visualizing algebraic functions. HighFour History of Mathematics Category A: Grades 4 – 5 Round 6 Wednesday, February 15, 2016 The use of calculator is not required. Answer #16: Explanation: Answer #17: Explanation: Answer #18: Explanation: Answer #19: Explanation: Answer #20: Explanation: Negative numbers Negative numbers are real numbers that are less than zero. The Chinese are the first mention negative numbers, back in 200 B.C.E. They used the rod system to perform problems with negative numbers in it. Negative numbers appeared in issues dealing with currency. Although negative numbers are mentioned they are not fully acknowledged as an existing value. Girolamo Cardano Girolamo Cardano, lived in the 16th Century and is known as the “The Father of Probability”. He lived in Italy and was a renaissance mathematician. He made many contributions to the field of Algebra and is credited with introducing binomial coefficients and the binomial theorem. Irrational numbers All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-­‐repeating digits to the right of the decimal point. Perimeter Perimeter is the distance around a two dimensional shape. It comes from the Greek word ‘peri’ meaning around, and ‘metron’, which means measure. Its first recorded usage was during 15th Century. Heron’s Formula In geometry, Heron’s (or Hero) formula states that the area of a triangle whose sides have length 𝑎, 𝑏, and 𝑐 is 𝐴 = 𝑠 𝑠 − 𝑎 𝑠 − 𝑏 𝑠 − 𝑐 where 𝑠 is the semi-­‐perimeter of the triangle. The formula is credited to Heron of Alexandria, and a proof can be found in his book, Metrica, written c. A.D. 60. It has been suggested that Archimedes knew the formula, and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible that it predates the reference given in the work.