Lisa's Blog

  If we acknowledge non-European sources of mathematics, I believe students can have an opportunity to view mathematical topics in many different ways and perspectives.  Ancient Greek’s math focused more on logic and great details were involved to prove propositions. They focused on proving mathematical ideas. Chinese math was more interested in providing solution to announced problem. They were interested in memorization, but proof was not provided. Since both of ancient Greek and Chinese mathematical knowledge were similar, students will be beneficial by looking at non-European sources of mathematic rather than only learning European sources of mathematic.    I think named theorems can guide students to have some limited mathematical facts. When we think about right angle theory, both Chinese and Greeks mathematicians made discoveries, but contribution of Chinese mathematicians were ignored, and Pythagoras and Archimedes are only well known mathematicians.  

  Eye of Horus was the symbol representing protection, health, and restoration in ancient Egypt. It was also used in amulets as according to Egyptian myth, Horus lost his left eye when he had a struggle with Seth, Egyptian god. His eye got restored by Hathor and this restoration became a symbol of healing.   Unit fractions ½, ¼, 1/8, 1/16, 1/32 and 1/64 are associated with the parts of the Eye of Horus. Each part represents to human six senses which are smell, sight, thought, hearing, taste, and touch.   ½ represents smell, triangular shaped object can be found which resembles human nose, ¼ represent sight and central round-shaped in Eye of Horus resembles shape of massa intermedia. 1/8 represents thought, eyebrow shaped in eye resembles shape of corpus callosum. 1/16 represents hearing, triangular shaped object in eye resembles Brodmann areas (center of hearing in humans). 1/32 represents taste, tail shaped object in eye resembles taste pathway, and 1/64 represents touch...

  Egyptian Problem:   Twice the quantity and its fifth, added together, give 22. What is the quantity?   Modern solution:   2x +  x/5  = 22,     11/5x = 22 , x=10   Egyptian “False Position”   Try x=5   2x +  x/5 = 10 + 1 = 11   We need 22, which is twice as big. So x must be twice as big as the trial number.   5  *  2 = 10     Check: if x=10, 2x +  x/5  = 20 +  10/5  = 20 + 2 = 22

  I could learn a lot of things through this group work. Firstly, it was nice time to review some definitions of terminologies especially sagitta. Moreover, it was nice to know formulas for finding sagitta and chord that are needed when we want to find them in each circle. Our group had to derive those two formulas by modern way and an ancient way. By deriving in a modern way, I could understand well how formulas can be found by using Pythagorean theorem. By deriving in an ancient way, it was nice to know that it is possible to derive it by using an ancient way and we can still get the identical formula.     I could also learn about ancient Babylonian history of the segment of the circle. I was nice to know that they started to study the properties of a circle such as area of circle. Also, I learned that Babylonian believed that relation between diameter and circumference of circle was c=3d where c is circumference and d is a diameter. Moreover, they approximated the pi a...