HighFour History of Mathematics Category A: Grades 4 – 5 Round 5 Thursday, January 12, 2017 The use of calculator is not required. Question #1: Question #2: Question #3: This irrational number, 1.61803…, is a well-­‐known ratio, which is used to analyze the proportions of natural objects as well as man-­‐made systems, such as financial markets. What is this ratio called, which is represented by the diagram shown? Graph theory in Mathematics is the study of points and lines. This historically notable problem, solved by Leonhard Euler in 1736, required to devise a path through a city that would cross each of the bridges only once. What is this problem known as? What geometrical shape does the following definition describe? “It is a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points is constant.”
Question #4: Question #5: This devise is also known as “counting frame” and as its name suggests, it has been used as a simple calculating tool for several centuries. This device, as we know it today, has been used in China since the 14th century. What is it called? In the movie 'The Wizard of Oz', Dorothy, The Lion, The Tin Man and The Scarecrow wanted a gift from the great Wizard of Oz. The Scarecrow wanted a brain. When he finally got one, he pronounced, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” Although he stated the theorem incorrectly, which theorem was he trying to say? HighFour History of Mathematics Category A: Grades 4 – 5 Round 5 Thursday, January 12, 2017 The use of calculator is not required. Question #6: Question #7: Question #8: Question #9: Question #10: It is claimed that the priest architects of Egypt could lay out a right angle with the aid of a rope divided into a ratio by three knots. What is this ratio, which is also considered the earliest form of the Pythagorean triplets? This mathematician is considered one of the greatest mathematicians of antiquity. He calculated the area under the arc of a parabola and gave a remarkably accurate approximation of the number 𝜋 (pi). Who was he? The five-­‐pointed star shown is drawn with five straight strokes. It contains ten points (the five points of the star and the five vertices of the inner pentagon) and fifteen line segments. What do we call this two-­‐dimensional figure? In 1557, just a year before he died, this mathematician introduced the today commonly known equal sign (=) and introduced the pre-­‐existing plus sign (+) to English speakers. What was his name? Temperature in everyday life is commonly reported in one of two ways: in degree Celsius (C) or Fahrenheit (F). The formula to convert from on system to the other is given as follows: 9
𝑇# = 𝑇' + 32 5
where 𝑇# represents the temperature in Fahrenheit and 𝑇' represents the temperature in Celsius. At what temperature are Celsius and Fahrenheit equal? HighFour History of Mathematics Category A: Grades 4 – 5 Round 5 Thursday, January 12, 2017 The use of calculator is not required. Question #11: Question #12: Question #13: Question #14: Question #15: This measuring instrument is used to determine the area of an arbitrary two-­‐
dimensional shape. The first modern version of this device was built by a Swiss mathematician in 1854. What is it called? The system of numbers 1, 1, 2, 3, 5, 8, 13, 21, … is named after an Italian mathematician who lived in the first half of the 13th century. He was considered the most talented Western mathematician in the Middle Ages. What was his name? This English mathematician was born in 1643 and went on to build the first practical reflecting telescope, shown. He is recognized the the most influential scientists of all time and a key figure in the scientific revolution. What was his name? In 2006, this toy was created by Jay Horowitz in Ohio, USA. It is a variation of Rubik’s Cube in which the faces have numbers one to nine on the sides instead of colors. What is this toy called? The essay “A Mathematician’s Apology” was written in 1940 by a British mathematician. One of its themes is about the aesthetics of mathematics regardless of its usefulness in practical applications. Who was this mathematician? HighFour History of Mathematics Category A: Grades 4 – 5 Round 5 Thursday, January 12, 2017 The use of calculator is not required. Question #16: Question #17: Question #18: Question #19: Question #20: This toy was invented by Ernő Rubik, the inventor of Rubik’s Cube. It has 24 wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts so that they can be twisted but not separated. What is this toy called? The author of Alice’s Adventures in Wonderland and other stories was a well-­‐known mathematician in the 19th century who slipped several mathematical ideas and puzzles in his stories to amuse children. What was his real name? This mathematical game or puzzle consists of three rods and a number of disks of different sizes. The objective of the puzzle is to move the entire stack of disks to another rod by following simple rules. What is this puzzle called? In its classical and modern forms, this alphabet has 24 letters, ordered from alpha to omega. Like Latin and Cyrillic, this alphabet originally had one single form of each letter, however, it developed the letter case distinction between upper-­‐case and lower-­‐case forms in parallel with Latin during the modern era. What is this alphabet known as? In Mathematics and Computer Science, this number system is widely used. It contains two digits, typically 0 (zero) and 1 (one). Because of its straightforward implementation, this system is used internally by almost all modern computers. What is this number system called?