Pythagoras

When I was in the second grade, a car struck me and sent me flying 117 feet in the air. The survival from this accident was due collectively to the combined prayers and diligence of family, friends, doctors, and a community filled with LOVE.

I learned to walk again late in the third grade. In October 1966, a wonderful tutor by the name of Doris Hughley introduced me to wondrous things, including cursive handwriting and higher-level reading techniques. Sensing my strong mathematical abilities, Mrs. Hughley also introduced me to circles, rectangles, functions, and the Pythagorean Theorem (c-squared = a-squared + b-squared).

She gave me an age-appropriate biography of Pythagoras. Six things impressed me most about this man (Math Open Reference).

All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics.
The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Pythagoras believed that both mathematics and music could purify.
Numbers have personalities, characteristics, strengths and weaknesses.
The world depends upon the interaction of opposites, such as lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow.
Certain symbols have a mystical significance; and
All members of the society should observe strict loyalty and secrecy.

My life and recovery continued based on Christian faith and the wholly compatible teachings of Pythagoras and other intelligent people. My college education centered on the fundamentals of business and finance, but the study of mathematics continued along with Philosophy, Statistics, Sociology, Physics, Psychology, and Poetry. There was even time for a new discipline – Computer Science – along the way. It seemed like all of the study had a common requirement intertwining mathematics into the discipline.

Upon the conclusion of graduate studies at SMU, the professional stage of my life commenced. The next 40 years introduced me to investment banking, valuation analysis, and financial management. Each of these disciplines require heavy mathematical training, but the fundamental math principles taught to me by Mrs. Hughley long ago (including the Pythagorean Theorem) continued to have a fundamental feedback. I also continued the study of Pythagoras. It humored me that a person who devoted an entire life to precise analytics could have an estimated date of death between 500 BC and 475 BC.

Then in 1987 I met the love of my life and entered into a marriage to Beth that has filled life with joy. Life blessed us with two wonderful daughters. As each daughter developed comfortably in their mother’s womb, I recited the Pythagorean Theorem nightly to each child. Beth is convinced that these nightly math readings contributed to each daughters’ musical, analytical, and problem-solving skills to this day!

In 2015, it was a privilege to study with Dr. Ashwath Damodaran, one of the greatest minds in the field of Valuation. I laughed when I first read his name because Pythagoras’ only daughter was named Damo.

Late in 2019, I had a business associate wanting to do business within a ten-mile radius of his primary residence. I obtained a map and legend and a protractor from the 8^th grade and drew the circle. Being a stickler, the client’s lawyer asked me to calculate the circumference of the market area but he didn’t trust that pi was an appropriate constant to use. He had no proof that 3.14159265358979… was correct. SO, the challenge was on: I had to develop a Rock Solid Proof of PI.

The epiphany hit me in the middle of the night, shortly after 3:14 AM. The Pythagorean Theorem could be applied within a circle to create a right triangle with tangential points on the sides of the circle, The hypotenuse of the triangle would be the first approximation of ¼ of the circumference of the circle. Since the radius is known, PI could also be roughly estimated. I then created a second right triangle from the first and produced a more precise estimation of circumference and Pi.

The same right triangle logic was replicated for 1000 iterations. Lo and behold, the calculated value of PI is 3.14159265358979…

Please reply to this Post and I will gladly send you a copy of the mathematical iterations for the Proof of Pi. The original concept for the Pi Proof (created on the back of a Sudoku Puzzle) appears at the top of this Post. In case you are interested in the accuracy of my Market Area Pi Proof, the circumference of the client’s Market Area question yielded a circumference of 62.8318 miles and a market area of 314.159 square miles. Assuming 20 customers in each square mile, the client has 6,283 customer opportunities ready to make a purchase. Isn’t Math FUN?

https://www.mathopenref.com/pythagoras.html