## Leonhard Euler

How Imaginary Numbers Were Invented

Ela Nur Halil

Luca Pacioli, Leonardo da Vinci’s math teacher published Summa de Arithmetica in 1494. It consisted of all math known in Renaissance Italy. One chapter was devoted to the cubic equation. Pacioli came to the conclusion that solving it was impossible.

Why You Should Never Play the Roulette in a

Casino

Poyraz Ali Güner

Rules of Roulette:

Choose a number, any number. Heck, choose as many numbers as you want! This is the main premise of a traditional roulette table if it were to be told to a 5-year-old.

The Math Behind Artificial Intelligence

Doruk Alp Uzunarslan

Do you ever realize how often you use the assistance of artificial intelligence? In daily life, especially for younger generations, people tend to visit various websites throughout the day. Either knowingly or unaware, artificial intelligence (AI) system algorithms guide its clients. Those algorithms mostly depend on some math functions. So let’s dive deeper about those.

Knight's Tour Problem - The Adventure of a Knight

Derin Değerli

In the intricate art of mind games, there exists an extraordinary dance between chess and mathematics. The strategic scheme behind chess consists of numerous math phenomena, including geometry, game theory, optimization, statistics, and number theory. There is one particular intriguing problem that piqued my interest regarding the relationship between chess and mathematics: the knight’s tour problem. The knight’s tour problem is an old puzzle where the knight makes legal moves on a classical chessboard (8x8) to visit every tile exactly once in one rotation. The animated model below offers a visual demonstration of this problem.

The Math Behind Neural Networks

Hüseyin Eren Arslan

For the past decade, artificial intelligence has become a huge part of our lives. Even if we do not use it directly in our daily lives, it is used to analyze, extract, and come up with its own decisions. But what does artificial intelligence exactly do, how does a machine learn just from a sample of data? It basically uses certain mathematical functions to extract data and come up with either a decision or a value. In this article I will focus on the concept of Neural Networks, Convolutional Neural Networks and the mathematical functions used.

Can Incompleteness Complete Mathematics I: The

theory and how Gödel proved it

Erdem Akder

This is the first part of the article about Gödel’s theory of incompleteness. This part will delve into the theory and the methodology that Gödel followed to demonstrate that mathematics is incomplete. The second part will concentrate on the implication of the theory and its relationship with epistemology and physics.

The Mystery of Infinities

Emir Alikalfa

In the mysterious realm of mathematics some concepts ,such as infinity, catch people's attention and make people wonder about itself. Georg Cantor was just one of many mathematicians who were intrigued about the term “infinity”. But, what actually is infinity?

###### Articles From Last Years

###### Math and Earthquakes

Ceyda Toprak

Do you know the relation between earthquakes and math? If you would like to know, let’s learn together.

###### Infinity Minus Infinity

Seden Nalbant

Any number subtracted from itself is equal to zero. Therefore, you might think that infinity minus infinity is also equal to zero; however, this is not true. Let’s find out the answer together.

###### Why is 0! Equal to 1?

Özdoğan Çağrı Dirik

First of all, let’s define factorial. Factorial is a function of any natural number that multiplies all the counting numbers less than or equal to itself. The factorial of the number “n” is represented as n! and it is equal to the following expression:

## Let's Get Variational

Eda Toprak

Before delving into calculus of variations, let’s look at a more familiar topic. How would you find the local minimum in a function f(x)?

First, you would derive and then equalize to 0. Then, finding the values of x satisfying this equation would be candidates for local min. As the solutions of = 0 leads to the stationary points, further testing allows the determination of the nature of these points. In this problem, we are concerned with the single variable differential calculus.

## Magic Squares

Poyraz Ali Güner

Figure 1: A Magical 3x3 Square

Imagine waking up in a room, finding a plane with a 3x3 grid painted on it, balanced on a little marble with 45 cubes next to it. To get out, you must arrange the cubes in such an order that the sums of blocks in every line, colon, and diagonal in the grid should exactly be the same, causing the plane to be in balance.

## Gabriel's Horn

Ezel Göktaş, Recai Efe Sunay

Figure 1: Gabriel's Horn

In this article, the underlying mathematical understanding of “Gabriel's Horn” is evaluated. According to some religious beliefs, Gabriel is supposed to blow his horn and announce Judgment Day when it comes. However, there is a notion that is unique and peculiar about the understanding of his horn when it is approached as a geometric figure.

## An Introduction to Abstract Algebra: Binary Operations

Ahmet Eren Doğan

Figure 1: Binary operation combines x and y

The word “binary” means consisting of two pieces and a binary operation is a rule for merging two values to obtain a new value. The operations such as addition and multiplication that we all learned in elementary school are actually the most common binary operations.

In order to understand binary operations, we first need to look at the definition of a mapping which is very similar to a function.

###### Matryoshka

Ece Paksoy

Let’s choose a number - for example 7. Then square that number - which gives us 49 in our case. Then square the resulting number and continue until we find a repeating point or a boundary. Unfortunately, if you have chosen a number bigger than 1, you would have seen how quickly it started to increase without any limits. However, if you have chosen a number between 0 and 1, like , the number becomes smaller and smaller and remains in a bounded place. But if we had chosen a negative number like -5, it would have also blown up and would have gone to infinity. So, which numbers do stay in place and remain in a bounded area when we constantly square the ending result?

###### The Golden One

Ada Ayas

Numbers are also the language of harmony. Whether in the field of painting, in architecture or in the world of sounds, people have tried to express harmony in the language of numbers. The throne of beauty in the visual field is based on a wonderful number: the golden number.

is one of the two roots of the equation .

The decimal value of this number is 1.618. Wherever people look, they want to see this number.

###### A Basic Introduction to Fractional Calculus

###### Zanyar Oğurlu

What does it mean to find a derivative of a function at a certain value? It means finding the slope of the line that is tangent to the function, or rate of change, at that point. What does it mean to find the second derivative of a function at a certain value? It means finding the rate of change of its slope, or the curvature, at that point. Here is the tricky question: How do we find the nd derivative of a particular function? What does it even mean to perform such a calculation? Well, it means very little. It means something very rarely, like, maybe if we are dealing with very complicated fractals, it can mean something then. Other than that, it is just fun to think about, which is the motivation behind this article.

Logistic Curves

So we were saying that the epidemic does not continuously grow at the exponential rate, yet it slows down and thus concaves down after the inflection point, which is where the shape changes from concaving up to down. Since the analysis of COVID-19 worldwide leads to logistic growth eventually, let’s further investigate logistic curves. The formula of a logistic curve would be...

# How to Bake Functions from Scratch

Ece Paksoy

In physics, to find how a pendulum behaves the equation T(1 - cosx) - x being the angle between the equilibrium position and the rod, and T being the length of the string- is used. However, to help the students solve problems without their calculators, their teacher shows them another equation that looks like and substitutes cosx with . When we plot both functions, they do resemble each other for small angles near zero but how can we even think to find these approximations?