Eye of Horus and unit fractions in ancient Egypt.

Apparently Seth who was Osiris' brother killed Osiris and his son Horus fought and killed Seth as retribution but lost his eye in the battle. Part of his "Eye" was restored by the god Thoth though. Egyptians then used fractions of 1 divided by the 6 powers of 2 for grain which are represented in the eye although this may not be accurate. 

As for myself I wouldn't say there are many numbers that have a special meaning to me other than number 9 which is the number I grew up wearing in competitive sports and tends to be my number of choice when doing any activity now. 

Constructing a magic square

 When constructing the magic square I decided to break it down into several steps otherwise the dask was a bit overwhelming. 

Attempt #1

As you can see for attempt #1 I decided to tackle the top row first in my head I went through going 1,2,3,4... etc. through the table and saw that it would not work leading me to put 1 in the middle column as I figured it would be easy to work downwards and 8/6 on the ends as they were easily divided by 2.

Attempt #2 

For attempt 2 I worked down from 1 as it was quite simple I used 5 in the middle as I knew I could use 2 in the bottom right to make 15 with the 8 and that 9 at the bottom would make 15 down. 

Attempt #3

I decided to fill in the bottom as I could finish off the diagonal as well I knew 4 in the bottom left would make 15 leaving me with 2 in the bottom right ot make 15 across and diagonally both ways. 

Attempt #4

The easiest attempt I only had 3 and 7 left and they fit perfectly on the left and right respectively creating 15 across each column and row and of course diagonally 

Was Pythagoras Chinese?

 I personally believe it is very important for teachers to acknowledge non-European sources of mathematics especially since Canada and Canadian classrooms are so diverse in race, gender, and religious beliefs. I believe making the material more relatable to all students is beneficial and important. It also provides certain individuals with a connection to certain material and theories hopefully translating to a better learning experience. I believe it is difficult to say that Pythagoras and the triangle was Chinese as there is evidence that the knowledge used was based off several other mathematicians and is often called other names in different cultures. Although I do believe Pascal deserves some credit but believe that it is important to teach people of the true history. 

False Position

I believe the false position is unique in the sense that it doesn't give you the solution but rather allows you to come up with an easy answer into what x equals. 

e.g. An Apple store will sold some of their Iphones this week and had 2000 Iphones in stock. How many Iphones did they sell this week if they have 1500 remaining in stock? 

Try x = 250

2000 - x = 1500

Since X = 250 that would leave them with 1750 remaining Iphones (250 more than what was sold) so if you double x = 250*2 you will get 500 

2000 - 500 = 1500

History of Babylonian Word Problems

 

When reading "The History of the Word Problem Genre" I was shocked at how similar the word problems look to what I have taken in high school along with calculus at UBC, overly complex, filled with unnecessary words and almost like solving a puzzle. I have always found it interesting when teachers, students etc. reference the idea that word problems are "real world" situations but many of the word problems outlined in the reading and ones I have done myself represent nothing close to what I have used mathematics in the real world for. Given my studies for the last four years (Finance) have revolved around mathematics it would seem logical that I would be an advocate for word problems but in reality the problems I have solved on the job or in daily life using mathematics have either been fairly straight forward and have non-complex language making it much simpler to solve or alternatively the problems are not laid out or described and rather must be developed by myself or another individual to even begin solving them. 

Although math problems we see today are complex and abstract they are not as abstract as the Babylonian problems I believe this largely has to do with the fact they did not poses a refined system like algebra that we have now adopted and is used daily. Rather they had to represent math in real life situations and likely situations they had seen previously and have had trouble solving. 

Applied mathematics is obviously important as it allows students to use real world applications and solve problems in an ideal manner and hopefully easily. Pure mathematics on the other hand though complex and less logical is still very important as it develops a way of solving much more complex problems that you may not see everyday but could potentially run into; furthermore, pure mathematics is becoming ever more prevalent with the development of technology and the advancement of society. 

Assignment #1 Solutions

 Pythagorean Theorem: 

x^2 + y^2 = z^2 

Solve for the number of solutions for 100:

Number of solutions = 30 

E.g. y = 2499, z = 2501

Solve for the number of solutions for 210

Number of solutions = 54 

Eg. y = 11,024 z = 11,026

Solve for the number of solutions for 420 

Number of solutions = 162 

E.g. y = 44,099 z = 44,101

Solve for the number of solutions for 35 

E.g. y = 612 z = 613 

Extension of the problem!

Can you solve for the number of solutions for x = 5? 

Answer: 

2 solutions including y = 12, z = 13 and y = 0, z = 5