If . . . then . . .

Andy B. Hook

• Publisher: Resource Publications
• Year: 2021
• Print ISBN: 9781666715323, 9781666715330
• eBook ISBN: 9781666715347
• Topic: Littérature
• Subtopic: Poésie religieuse

Mathematics has always been humanity's best tool for understanding the world around us. From the farmers of ancient Egypt to the astrophysicists of today, we have used math to analyze and study our universe, and it has been incredibly successful. And yet, so few of us have ever been exposed to the beauty and wisdom that can be found in math. This work is an attempt to give the reader an insight into the beauty, the creativity, and the wisdom that can be found in a field that all of us have studied, but so few of us appreciate.

Axiom #1

I am the same as you

You are the same as me

If I am the same as them

They must the same as you

And you them.

This is the nature of equality.

Axioms #2 & 3

Things begin equal.

If they gain

The same

Or lose

The same

Equals remain equal

This is the basis for maintaining balance.

Axiom #4

We are what we are

Neither more nor less.

A thing is equal

To its self.

How could it be otherwise?

Axiom #5

The whole is greater

Than the part.

The branch needs the trunk for support.

The trunk needs the branch for sustenance.

The tree needs only the sun.

What is a leader without a pack?

Tesselation

(Pythagoras)

A shape

Can be divided

Into triangles.

Which can be divided

Into right triangles.

Which are comprised of

Line segments

Which form the foundations

Of squares

The areas of which

Sum to one another.

Thus, the simplest shape

Provides the way

To all others.

Pythagorean Triplets

Think of two numbers.

Square them and

Find the difference

Of the squares.

Call this A.

Multiply...

Table of contents

• Title Page
• Q: The Rational
• Point
• Definitions & Dimensions
• Postulate I
• Postulate II
• Postulate III
• Postulate IV
• Postulate V
• 5th Postulate Revisited
• Axiom #1
• Axioms #2 & 3
• Axiom #4
• Axiom #5
• Tesselation
• Pythagorean Triplets
• 3 Problems
• A Famous Death
• R: The Real
• The Fundamental Theorem
• Limits
• Continuity
• Gauss’ Equation
• Geometric Series
• ex
• dx/dy
• Intermediate Values
• Mean Value
• Taylor Series
• The Squeeze Theorem
• Strange Attractors
• Turbulence
• Fractals
• N: The Natural
• Primes & Composites
• GCD (a,b) = 1
• Congruence
• Phi(m)
• Infinite Primes
• Goldbach’s Conjecture
• Quadratic Residue
• Infinite Descent
• Sum of Two Squares
• The Phi Function & the Sum of Divisors
• Gaussian Integers
• √p≠a/b
• The Law of the Excluded Middle
• Transcendentals
• Pascal’s Triangle
• Mordell’s Theorem
• Heptadecagon
• C: The Complex
• {ø}
• ∞
• Euler
• Russell’s Paradox
• Sets
• Sets → Groups
• 1 Identity
• 2 Inverse
• 3 Associativity
• 4 Closure
• Complex
• A Dialogue
• ÷ 0
• Gödel 2
• Gödel 1