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!

Alice in Wonderland

The 11th book that I have read is Alice in Wonderland by Charles Lutwidge Dodgson (aka Lewis Carroll), which, despite its title, is suitable for both genders. Like all the other books I have read, the story is filled with adventure. 5/5!

Here is the summary of the story.

A young girl named Alice finds that a white rabbit is rushing to some kind of event. She follows him down the rabbit hole and finds that she is too small to enter a door she wanted to enter. She finds a key for that door and finds a drink that would shrink her. She realizes that she left the key on the table and eats a cake that makes her nine feet tall! She soon sees after a few moments that she is now in a forest and keeps on changing sizes throughout the story. She also finds out that everyone in the forest is insane. After a tea party with the Mad Hatter and the March Hare, she enters the small door from earlier into a garden. The Queen of that land offers Alice to play croquet, with flamingos as mallets, hedgehogs as balls, and two playing cards with heads, arms, and legs as the arches. She executes many players to settle the arguments. Afterward, they are in a trial where the Knave of Hearts is accused of stealing the tarts (obviously from the nursery rhyme). Alice soon snaps out of her daydream.

-End of Summary-

Side note: the “1 in 45 chance” from the previous entry/review involves a mathematical concept called factorials.

Here’s how it’s done:

___n!___
(n-r)!r!
With 10 as n (number of items), and 2 as r (books I didn’t like), this is the new structure:
___10!___
(10-2)!2!
We can simplify further:
___10!___
8!2!
Solving for the factorials by canceling out the factorials, we get:
___90___
2
90/2=45. It is a 1 in 45 chance.

Because I have read 11 books, the chance becomes less likely (1 in 55).

If this is too confusing, ask me to explain it further. J