The Most Beautiful Mathematical Formulas

With around 50 formulas, this is a must for future mathematicians. 5/5!

Part 1: Powers of Numbers (Form. 1-2)
This very concise part explains about the powers of numbers (any number!) Also, it explains that (x^n)(x^m) = x^(n+m).

Part 2: Tri., Rect., Squ., and Cir. (Form. 3-10)
This part contains the innovative geometric discoveries. Things such as the areas of geometric figures, the rediscovery of the Pythagorean Theorem, and equal proportions in which rearrangement of areas of a square doesn’t make a difference.

Part 3: Angles (Form. 11-15)

This section talks about the proportion of the sine of an angle to its cosine. Also, it explains how the number pi (3.1415926535897932384626433832795...) is approximately 355/113, despite the fact that pi is irrational.

Part 4: Quadratic Equations (Form. 16-18)
It explains the Golden Ratio used in quadratic equations, the roots of a quadratic equation, and imaginary numbers. This is again a very concise part.

Part 5: Logarithms and Exponentials (Form. 19-28)
It describes the discovery of logarithms, how to find logarithms, the number e, that number raised to real and imaginary power, and that e to the i*pi power=-1.

Part 6: Series of Numbers (Form. 29-34)
This is probably one of my most favorite sections in the book. It has paradoxical equations, such as ½+¼+1/8+1/16..., the Fibonacci Sequence, permutations, 1+2+3+…_+n= n(n+1)/2, and more.

Part 7: Objects in Space (Form. 35-39)
This explains the theories about 3-D figures like cubes, spheres, pyramids, and prisms. It contains the formula of the surface area and volume of a sphere. It also has Euler’s Theorem: the faces on a 3-D figure -the edges + the number of vertices (corners).

Part 8: Whole and Prime Numbers (Form. 40-44)
This is probably my favorite section out of the entire book. Lagrange’s Theorem explains that any number is the sum of four squares. More topics are the facts that prime numbers are indivisible except for itself and 1, the Goldbach’s Conjecture, stating that every even number (except 2) is a sum of two primes, and Fermat’s Last Theorem.

Part 9/10: Chance/ Today and Tomorrow… (Form. 45-47, 48-49)
These two sections are so concise that they can be summarized in one whole piece. It has the chance of winning the lottery, Pascal’s Triangle, betting on roulette, the binary system, and the book-ender: the concept of infinity.

I hope you find this book somewhere and enjoy it! That’s all for now!