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Visualized: An Appreciation

Meant as an accompaniment material, “Visualized: An Appreciation” is a compilation of different examples used for the 3 topics displayed, namely: Game Theory, Fibonacci Sequence, and Fractals.

It showcases the pictures of the examples in a way to aesthetically present math’s remarkable appearances in our mundane lives. Here is a link to the full PDF, which is meant to be read alongside the blog articles.

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Fractals

Coined by Belgian mathematician Benoit Mendelbrot in 1980, he used the word “fractal” due to the fractional nature of the Fractals.

These are patterns that involve the duplication, shrinking, and re-positioning of a certain object into the original sized object. It displays a seemingly never-ending pattern created by the single object

Its presence in nature is in the snowflake and the way trees grow; and in architecture that supports structures. It often poses as a hypnotic and aesthetically pleasing phenomena to many.

The Shah Mosque, built in 390 BCE. It shows the prowess of Islam architects, mathematicians, and artisans through the beautifully constructed place of worship.

Here is a link to the accompanying scrapbook/collage, which is meant to be read alongside the blog articles.

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Fibonacci Sequence

The Fibonacci Sequence is a sequence made from the sum of two consecutive numbers. The numbers within the sequence are known as “Fibonacci numbers” and they make-up the sequence as you add the two consecutive numbers together

Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it.The 2 is found by adding the two numbers before it (1+1) The 3 is found by adding the two numbers before it (1+2), And the 5 is (2+3), and so on...

In photos, it appears as a conical shape that expands from the inside out. It gives a tangible picture of how the sequence works

The Golden Ratio

The Golden Ratio is the ever-present number in the Fibonacci Sequence. It is 1.61803... a never ending number that is actually present between two consecutive numbers. 

when you divide the numbers, the result is also a number close to 1.61803, whether its a bit higher or lower.

This application is most commonly upheld by nature, and applied in photography, graphic design, and even architecture.

Here is a link to the accompanying scrapbook/collage, which is meant to be read alongside the blog articles.

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GAME THEORY

Game Theory is known as the study of strategic decision making in situations called games. In this article, we are going to talk about the different classifications of games, under which some of familiar situations fall under! It can be noted that one can use strategy for any situation they fall under, regardless whether or not it is an actual video game. All that matters is that there is a specific way one tries to tackle the situation and how they aim to gain a desirable payoff with the nature of the situation.

Try and see if any of your daily activities can be classified.

The Classification of Games

Randomness

Games that could contain random events which can influence the outcome of the game and the player’s payoff

Example: Wario Party Gold on the 3DS uses micro games or mini games to allow the player to ascend through the different tiers of Wario’s tournament 

Here’s a clip showcasing the tournament-style mini games where the player can play to win the potluck or fail and lose the tournament

Cooperative

Games where among the players there are groups that are formed that allows them to all share the same payoff.

Example: Team sports like basketball, volleyball, and football are prime examples of cooperative games due to the teams having strategies that depends on their interactions and cohesiveness.

Non-Cooperative

Individual players make decisions and strategies that would benefit them and them alone

Examples: The men’s division of figure skating at the Olympics is an example of each individual skater skating along to a program they all devised for themselves as it emphasizes their strengths.

Here is the free skate performance of Shoma Uno at the Grand Prix Final, which won him the bronze medal

Zero-Sum

A game where only a single player can have a positive payoff and everyone else would lose.

Example: “The Game” is one where whoever thinks, speaks, or is thinking about “The Game” loses. The only way one person is able to win “The Game” is when they are not actively thinking/speaking about it or even not aware of it at all. As of you reading this article (after I had typed/posted it) we both have lost “The Game”, and will continue losing “The Game” until we stop thinking about it.

Sequential

Two or more players cannot move at the same time, but there are multiple moves for each player throughout the game. There are two types under this:

Complete Information: Persona 5 is a turn-based game where you fight enemies with different figures of mythology and history. You, your party members, and the enemy have turns to strategize and execute actions, and you are able to see the result of said actions as they happen. Here’s a sample clip from the game where you fight the first boss of the game

Perfect Information: Kerplunk! Is a game where players take turns removing sticks from a container w/ holes that carries marbles inside. The goal is to remove as many sticks possible with the least amount of marbles falling down. As each stick is removed, all players have the freedom to strategize the next stick they will be picking out because of the transparent nature of the container with marbles and sticks. Here is a clip of two popular youtubers known as Rhett and Link (from Good Mythical Morning) playing a giant version of Kerplunk!

Simultaneous

This is when all players have a single move that are executed all at the same time.

Example: Rock-Paper-Scissors is a game where you have to beat the other opponent in one round with rock, paper, or scissors. Rock beats scissors but loses to paper, Scissors beats paper but loses to rock, and paper beats rock but loses to scissors.

Here is a link to the accompanying scrapbook/collage, which is meant to be read alongside the blog articles.