May 442 Blog

• Consider the so-called Hardy-Ramanujan number 1729, and the story of Taxicab Numbers, retold on Wolfram Mathworld at the link above. Hardy is quoted as saying of Ramanujan that "each of the positive integers was one of his personal friends". What do you make of this in terms of Major's paper?   In this story , when the number first came into his mind he thought of it as a rather dull number,  adding that he hoped that wasn't a bad omen . However, as he thought about it, he found that “it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways" . In the paper, it is stated that each number has its own personality and people give them associations with good/bad fortune, heavy/light senses. Also, different numbers stimulate activity in a different area in the brain. So there’s biological reasons associated with our feelings about the numbers as well. For Ramanujan, probably he just had some different arrang...

Euclid was the founder of geometry. His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. I'm not good at interpreting poems but the first poem seems to talk about how Euclid found beauty in geometry findings, in shapes of shifting lineage, and this helped him experience the "flow" that releases him from dusty human bondage to luminous air. His  soul and his whole being  was lifted by this beauty, which gets him away from the human state and into a higher state of being. The next poem seems to disagree... and say that beauty is clothed, and say the first poet is an idiot. but I don't really get what he was objecting to .....and what he proposes instead!

Here is a link to our powerpoint :  https://docs.google.com/presentation/d/1infhLZ4Ow7wofXp-yRHw7PSjB_5yOkyrOllgYZgh5pY/edit#slide=id.g9a6108e0dc_10_32 In this project we looked at the fractals in art pieces and Indigenous designs,  and then developed a way to teach fractals using diagrams. I was in charge of the hypothetical class plan. I found the picture and labelled it. I didn't want to make it too hard for the first part of the class so I used a simple version of fractals. I asked them to measure the length and calculate the ratios.  I believe the first diagram is easy to manage/ understand. Then I led a class discussion to link the observations to the concepts. After that I led the lesson to a more complicated version of fractal tree. To make sure they understand the latter one, I asked them to draw a fractal tree themselves.  In this project I learned about how to incorporate art pieces into the math classroom. We could use graphics to teach certain concepts, ...

  4 3 8 9 5 1 2 7 6     To add to 15: 1+6+8 3+5+7 2+4+9 2+6+7 2+5+8   First fill in 2,5,8 as the diagonal Then fill in 6 and 7 at the bottom. since 7+8 exceeds the limit, use 6 for the column with 8 Using the two numbers present, fill in the rest. It works.       8   5   2 7 6

 Research online the significance of the Eye of Horus and unit fractions in ancient Egypt. What was most interesting to you in your findings? The Egyptian Unit fractions are based on the Eye of Horus. Horus was the ancient Egyptian sky god who was usually depicted as a falcon, most likely a lanner or peregrine falcon.[7] His right eye was associated with the sun god, Ra. It was believed by the Greeks and Romans that an evil heart could get to the eye. The thought to be powerful effects of eyes and optics created the myth that the energy-producing power of the eye had the ability to cast evil spells with just a glance. Because the ancients believed the evil eye could be counteracted with a 'good eye', myths about Horus arose.[9]  The eye of Horus was often used to symbolise sacrifice, healing, restoration, and protection.  I think the most interesting thing here is that the eye has so many connotations and it is something almost sacred in Egyptian culture. The an...

Adam gave Sam 45 dollars to buy groceries. He requires that the number of apples should be three times the number of bananas. The number of bananas should be double the number of oranges. suppose apples cost 2 dollars and bananas cost 1 dollar, and oranges cost 1 dollar, how many of each fruit should he buy? modern solution:  let the number of oranges be x.  x +2x+6x*2=45 15x=45 x=3 false position method: let x be 2  2+4+6*2*2=30 we need 45, which is 45/30=1+1/2 as big, so x must be 2 times 1+1/2 , which is 2+1=3 check: if x=3, x +2x+6x*2=45

 I think it is important to acknowledge non-European sources of mathematics because it promotes respect for other cultures. When only European sources of math are acknowledged, students tend to develop an understanding that only Europe is the origin of all creations in math/science. They would have unnecessary ego for their own ethnicity. When we acknowledge other cultures’ mathematical discoveries, we tend to have some level of humility, especially when some of the theorems claimed to be European are actually from China. For instance, “The method of the double-false-was first described in Jiu Zhang suanshu,indicating the method was known in China around 50 AD. Subsequently, the method was transferred to Muslim mathematicians at some point and then on to Europeans sometime during the Middle Ages. It then was brought back to China by the Jesuit missionaries, who claimed the method as their own.”   Also, “accounts and facts of Greek work during this time tilt more on the s...