Assignment 3: History of Coding

Our group's roadmap for the History of Coding and Computer Algorithms is below (the link is more useful, but the screenshot is the roadmap in full): 

https://prezi.com/elxw8xbxtwxd/?utm_campaign=share&utm_medium=copy

Explanation: 

The topic that our group decided to research is the history of coding and computer algorithms. What we noticed right away is that the history of programming languages has a couple key trends that we wanted to highlight through our format. Those trends are that, as with every other topic we have learned about throughout the semester, each succeeding programming language is influenced by or improves on a previous language in some way and that the core concept of coding is to make tasks increasingly simple and efficient. Furthermore, unlike many of the typical mathematics concepts, the development of coding has been rapid and is continuing to accelerate.  We also realize that computer programming is a quite recent development with the first programming language being in 1854, but the more significant advancements beginning in 1956 – less than 100 years ago. Given this, in addition to informing through the introduction of how and when each programming language was developed, we also wanted to highlight how quick the evolution has been and show how each language has been a building-block to its successors. Examples of this would be the development of Python, which is a successor to the ABC programming language or C++, which is an extension of the previously introduced C.

We found that these trends become obvious as we explore the progression of programming languages through time and that each advancement is quickly overshadowed or replaced by another. For this reason, we decided to keep the scope of our project very broad and display our findings through a roadmap that walks us through the history of coding. This way, we get to learn how coding has developed and the aforementioned trends will come to light as we move through time - the progression of coding has been swift, languages take ideas from previous ones and each succeeding language strives to become more simple.  We hope that this way, we will be able to cover the high-level important events in the history of coding while also highlighting how each event ties into each other. 

Assignment #1 Reflection

The first assignment was an interesting one for my group as we had no previous knowledge on the history of Pythagorean Triples and how far back they dated (1800s); furthermore, seeing what the Babylonian's were able to do with Pythagorean triples was quite interesting as it is a very sophisticated topic for their time. I personally found it quite interesting to see the tablets Babylonians were working on and just how different our world is compared to there's including simple things like writing on manufactured paper vs clay. 

My group was tasked with seeing how many potential solutions there were to our given problem, as we had no prior knowledge of the subject and how to tackle this we decided to use a form of brute force to find the solution. We decided to pick numbers for x etc. and solve for n and then apply the given number to the remaining numbers. Though this may not have been the most efficient method we were able to come up with the solution that we were able to back solve using excel after. I found this quite interesting as the Babylonians must have spent a significant period of time studying this concept something that is often over looked in todays classrooms. 

I also found it difficult for our group to decide on how best to teach this topic as none of us are in the education program and have no prior knowledge of teaching math (though I have taught snowboarding to children before). I found it interesting to see everyone's presentations and how they differed and have a new appreciation for how difficult it must be to come up with whole lesson plans that are engaging and thoughtful. 

Dancing Euclidean Proofs

 The Dancing Euclidean Proofs article was extremely interesting article and I found the discussion of the relationship between humanizing mathematics through dance fascinating and the video definitely assisted in creating that visual. In all honestly I wasn't very familiar with arts-based mathematics learning in any form but after reading about it in the article it makes logical sense as we obviously don't all learn in the same format and some are much more visual learners. I also found it interesting how easily Euclid's proofs lend themselves to dance as I always thought of geometry as visual in nature as I remember building cubes, triangles, etc. throughout school in order to better understand the concept.  I also found it interesting how the artists utilized the sand on the beach to draw these geometric shapes while dancing almost like a teachers whiteboard in a classroom but rather using the earth. 

Euclid

 

Euclid is considered the founding father of geometry in relation to his work in the textbook "Elements" which was used to teach math (specifically geometry) for a significant period of time. Although Euclid did not discover every aspect of geometry he was one of the first individuals to put the theory into a textbook for it to be taught further. 

When reading the poem by Edna I feel she is referencing how Euclid's mathematical findings had significant beauty and was admiring his work. I believe when she references "while they stare at nothing" is showing how individuals were viewing geometry prior to Euclid's discovering's and then she says "heroes seek release from dusty bondage into luminous air" perhaps referencing how free we became when Euclid published his findings as we now knew significantly more about geometry. 

I believe the second poem is perhaps thinking of a time prior to Euclid's discovery and saying how Euclid has seen the beauty of geometry but no one else had at the time leaving Euclid as the only individual to fully understand the world of geometry. I don't fully understand the second part of the poem but perhaps Edna is referencing other individuals who had discovered different elements of geometry and calling them idiots as they had not fully seen the beauty of it like Euclid. 

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.