David's Mathematical Blog

After reading the article, I can say that teachers should be acknowledging non-European sources of mathematics. I say this because of two points: Europe is not the only continent in the world, and there are often many ways to solve a problem, as demonstrated by the Pythagorean Theorem and the Gougu theorem. The motivations for solving mathematical problems were different in each area. For the Greeks, they used math to pursue philosophical truths of the world, and in doing so, put a much greater emphasis on proofs. The Chinese used math more in the application sense such as land surveying, but also acknowledged the existence of purely mathematical problems. As teachers, we should help the students understand why studying math is important to them, since all students are different in their own educational pursuits. My thoughts on naming mathematical concepts is that the concepts should be named after someone who contributed most to its discovery. I also think that we should not dwell on ...

Upon researching the Eye of Horus symbol, I learned that the Eye represented prosperity and protection, and it originated from a mythological battle between good and evil. Moreover, the Eye of Horus can be split into six pieces, each associated with a sense and a unit fraction: The 1/2 depicts a nose and represents the sense of smell. The 1/4 depicts a pupil and represents the sense of sight. The 1/8 depicts an eyebrow and represents the sense of thought. The 1/16 depicts an ear and represents the sense of hearing. The 1/32 depicts a rolled tongue and represents the sense of taste. The 1/64 depicts the somatosensory pathway to the brain and represents the sense of touch. I found it interesting that the sum of all these parts are very close to 1 (63/64), but cannot reach 1 based on these unit fractions alone. I hypothesize that there may be other components to the Eye of Horus that the Egyptians may or may not have accounted for, such that the sum of the unit fractions is 1. I cannot th...

The calculations involving a circle are usually very messy compared to other simple shapes such as triangles and rectangles. Going into this project, I was curious on how the ancient Egyptians calculated the area of a circle. I was surprised to see that they tried to fit the area of a circle inside a square with side lengths that was 8/9 of the circle's diameter. Looking back at my math classes, the teachers just gave me a formula with little to no explanation, just saying that it works. These experiences, along with many others, hindered my curiosity and appreciation for modern mathematics. I would have never thought to try to approximate the circle by an octagon, and especially, squaring the circle. Even though the Egyptians weren't completely correct in their methods, they were able to estimate extremely well using simple numbers and reasoning despite not knowing what pi is. Nowadays, I find that estimation and numerical reasoning is lacking among students, especially among ...

The sum of a quantity, half the quantity, a fifth of the quantity, a tenth of the quantity, and 32 is 57 and a fifth. What is the quantity? Egyptian way: First, simplify (very important) x + x/2 + x/5 + x/10 + 32 = 57 + 1/5 x + x/2 + x/5 + x/10 = 25 + 1/5 Try x = 5 (False Position) 5 + 5/2 + 5/5 + 5/10  = 5 + 2 + 1/2 + 1 + 1/2 = 9 Have 9, want 25 + 1/5, so divide 5 by 9, multiply by 25 + 1/5: 5/9 * (25 + 1/5) x = (1/2 + 1/18) * (25 + 1/5) = 25/2 + 1/10 + 25/18 + 1/90 = 12 + 1/2 + 1/10 + 1 + 7/18 + 1/90 = 12 + 1/2 + 1/10 + 1 + 1/3 + 1/18 + 1/90 = 14 Check: x = 14 14 + 14/2 + 14/5 + 14/10 + 32 = 14 + 7 + 2 + 4/5 + 1 + 2/5 + 32 = 57 + 1/5 Modern way:  x + x/2 + x/5 + x/10 + 32 = 57 1/5 9x/5 + 32 = 57 1/5 9x/5 = 25 1/5 x = 14