2024: A Mathematical Journey Into The New Year

The new year is upon us!

Any new year is characterised by a number. And when there's a number, there's mathematics.

This year, we have before us 2024.

This article presents the number 2024 in various creative forms.

These representations can be engaging and beneficial for students, teachers, researchers, and mathematics enthusiasts.

They also serve to enhance creativity in children and inspire a greater interest in mathematics.

So, here is 2024 in various, unique mathematical ways:

Simple Maths Operations

Let's begin by representing 2024 in multiple ways through the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 as squares, cubes, powers of 2, and factorials using all arithmetic operations like addition, subtraction, division, and multiplication.

Magic Squares

A magic square is a square grid filled with distinct positive integers such that the sum of the numbers in each row, column, and diagonal is the same. This constant sum is called the magic constant.

Here are some unique representations of fourth order, fifth order, eighth order, and eleventh order magic squares whose magic sum is 2024.

Fibonacci and Lucas Numbers

For the new year number, there exist these elegant summation expressions that use the Fibonacci and Lucas numbers to uniquely represent the number 2024.

The Fibonacci sequence is a series of numbers in which each number is the sum of the two that precede it.

The series begins this way: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and goes on.

Similar to Fibonacci numbers, Lucas numbers are also defined as the sum of the two numbers that precede it.

But unlike in the Fibonacci sequence, where the first two numbers are 0 and 1, the first two numbers in the Lucas sequence are 2 and 1.

Here are unique representations of 2024 as summations of Fibonacci and Lucas numbers:

Matrices

Matrices are arrangements of numbers in rows and columns such that they take the form of rectangular arrays.

The order of a matrix is represented as m x n, where m and n are the number of rows and columns, respectively.

We represent the new year number 2024 as a determinant of sixth order and fourth order matrices. Some special techniques were used to obtain these determinants.

Matrices are integral to mathematics, physics, and several other fields, and have various applications. 

Happy new year, and while you're at it, hope you have fun with some maths, too!