User:Wangfa10/sandbox

Introduction
Squaring the circle is an mathematical puzzle from the ancient Greece, the question is: could you construct a square with the same area as a circle using only straight edge and compass with finite number of steps； these are the rules that Ancient Greeks worked by.The difficult part for this challenge is that we cannot really measure/construct π, but we don't know that π is a number''' until 1882 when this challenge has been proven to be impossible to solve and the phrase "squaring the circle" has even become the metaphor for impossible things.

Impossibilty
With a straight edge and a compass, we could do addition:

we could do substraction:

we could do multiplication:

we could do division as well:

And the most we could do with a straight edge and compass is getting the square roots:

All numbers we could produce using the above methods are called construable number. Using circle with radius = 1 and try to calculate the square with the same area whose side length = root pi, we get this:

Turns out the problem is that we can't measure root pi/pi by straight edge and compass because pi is not either an algebric nor a constructable number, it is a transcendental number proved by Ferdinand von Lindemann in 1882, which has concluded it's impossibility.

Reflection
Before I start Mat402, I had been away from geometry for years and I never thought one day I will become a Wikipedia editor instead of a user searching random stuff just for a sudden interest or just have something intriguing across my mind; in this course, I was not only taught with a load of mathematical proofs and geometric knowledge but also how to edit wiki and interact with the professor and other students in this class through Wikipedia pages that are created by ourselves. In article 1, I was assigned to do Euclidean Book I Proposition 7, I had some knowledge about it because the prof talked about all the Euclidean Propositions one by one during the class and he also led us to do the wiki page set up and weekly wiki updates, using participation mark to get us familiar about how to use set up wiki page, post pictures, make references and design a wiki page with our own understanding and design. When we were about to write article 2, even the topic are way steeper and was not covered in the lecture, many are puzzles that are impossible to solve such as my topic, we still have the designing skills and self-thinking we've developed from Article 1 and now we are able to search internet, learn all the geometric ideas, gather all the information and with our own understanding to make a Wikipedia page about our topic. I believe the development of our self-learning and skills of making a valid mathematical research report by our own on a platform like Wikipedia is extremely valuable for us not only in this class but also to study further into mathematics and geometry in the future. Even though I did not do that well in this course, I still could say that I've learned much more than I expected, as a fourth year student, learning in the conventional way is already tiring for me and Professor Parker Glynn-Adey brought me something new and is very helpful for me not only improved by geometry but also in my web- developing and self-study skills which I will be valuable in my lifetime.