The Legend of Soh-Cah-Toa
Mental Princess of the Ages

by: S.K. Martz Copyright 2001 themathlab.com
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Part 1: She was born in the "far lands" deep in a secluded forest. Only her mother Catherine and the great spirit were aware of this special birth.


Her birth name was Sophia Catherine Zoe. To her people, names were sacred. They held the spirit of the present and the past. Each mother of a female child selected a name for her baby that embodied her dream for that child. By doing so, she passed a permanent blessing to the soul of the baby. Catherine's blessing for her baby was "wisdom" and so she named her Sophia.

When the females reached the age of maturity they would select their grown names. Catherine's birth name from her mother Mira, which means "beautiful", had been Zoe, meaning "life". Then when her mother died, and she was totally on her own, she chose for herself Catherine, meaning "queen of all".

So literally, the new baby's birth name/blessing, Sophia Catherine Zoe, translated to "wise queen of all life".

Part 2: The great spirit had told Catherine in her dreams that the baby inside of her was to be the most special female ever born. She was to be guarded and taught carefully for into her mind the great spirit would pour the most wonderful secrets of life.

Indeed little Sophia was a fast learner, and she had a warm loving spirit. Catherine kept her secreted away in the forest because the clans of the time were extremely violent. They did not accept outsiders into their midst easily. Often female babies were knifed to death as soon as they were born, if the male members of the tribe decided there were too many mouths to feed that season.

Part 3: So Catherine guarded Sophia carefully, just as Mira had guarded her. She taught her everything she knew about the forest and how to live off the land in secret, leaving no traces behind.

She made two little, right triangle, toys for Sophia out of sticks.

These were the trigon toys called Baba and Mama. They captivated Sophia's mind from the moment she could focus her eyes.

Sophia had a very happy beginning in life. It was just she and her mother and the forest animals. They moved a lot, but this only fueled her blooming intelligence.

Part 4: When Sophia was three her mind took flight. Her curiosity was insatiable. Everywhere she looked she saw patterns in nature. She noticed the five fingers on each hand and on each foot and developed a form of counting based on ten units.

She would doodle in the dirt like all little kids, but her doodles became numerals to represent the amounts she was counting, so that she could keep track of her results. Before long, she was adding and subtracting by using combinations of her little marks.

She also had the manual dexterity now to make herself some more trigon toys. She thought that Baba and Mama should have some friends so she made Oscar the bird clown, Bull, the rat trigon, Snar, the lizard trigon, and Thor, the wicked spike skin trigon.

She noticed that the ones with the skinnier noses looked meaner. In fact, Thor had the skinniest nose, and she made him the wickedest of all.

Part 5: By age five, she was truly involved in the development of number facts. She had written extensive addition tables and subtraction tables on countless pieces of dried bark and even etched the facts on flat stones. Everywhere they traveled, she felt she needed to leave a written record of the amazing patterns she was discovering.

She was also at this time developing simple multiplication and its reverse, division. Surprisingly it was Thor that got her thinking about the division. You see these toys had been her main forms of play all of her life and with her fascination of patterns, it was only natural for her to see that as the ratios of the rear sides and the bellies of her creatures changed, so did their personalities.

She felt that this relationship deserved a special name, so she called it the TANGENT relation. If the tangent decreased, the character got meaner. The nicest creature she had was a the funny old clown bird Oscar, and his tangent relationship was 2 to 1. The mean old Thor was 1 to 10. To describe these personality traits in terms of her secret symbols or numbers, she basically invented a secret code that we today call long division. She always divided in her code out four places past the decimal point, which she referred to as the point where mystery begins.

 

Part 6: At age seven, she discovered an amazing relationship. She was always particularly fond of her trigon called Mama. Mama had a tangent of 3 to 4, or in her secret code, of 0.7500. She was a warm loving, yet firm and strong trigon. While drawing pictures of Mama in the dirt one day, she happened to doodle some squares off of each of her sides. Using the multiplication that she had been working on, she realized that the area of the three square added to the area of the four square was equal in number to the area of the five square.

This of course is what we call the Pythagorean Theorem and it is a relationship that would later be "discovered" by every civilized society throughout history, but little seven year old Sophia Catherine Zoe found it first. She drew it as a tattoo on every tree she could find for miles and miles as she and Catherine traveled. Catherine is amazed.

Part 7: At age nine the problem of the Baba trigon, long side was solved. Sophia could not figure out what its length would be if the two smaller sides of the trigon were both one unit long. She needed to find a number that would multiply times itself and give TWO. Eventually, by a method of dividing and averaging she invented square roots!

Sophia's brain was developing faster than Catherine could understand. She feared for her safety; if anyone should ever find her, she would surely be burned or knifed as a witch or demon. Catherine prayed to the great spirit to protect her daughter. She also began to warn Sophia never to talk about these things if she should ever meet others.

Part 8: At age 10 Sophia developed the sine and cosine ratios. What began with her friends the toy trigons grew to a mania for unlocking all the secret codes of all the trigons she could make. It should be stressed here that her trigons were all right triangles, and that she did not use any fractional lengths on individual sides.

She realized that comparing the rear sides to the bellies or the "opposite sides" compared to the "adjacent sides", as she came to call them, was not the only way the sides could be compared. She decided to call the long, or top side of each triangle the "hypotenuse", it became her secret code word that meant, "longest side of a right trigon".

She invented the relationship SINE which meant the opposite side compared to the hypotenuse, and COSINE which meant the adjacent side compared to the hypotenuse. She then began the enormous labor of dividing out to four decimal places, each of these ratios, for every trigon from a mean pointy angle of 1 degree to the wide open angle of 90 degrees.

(She used a total division of a circle into 360 parts because of the 360 day year of growing that her mother had taught her. It seemed reasonable to cut any circle into 360 parts since the sun was a circle, and the sun controlled the growth cycle.)

The chart was quite impressive when it was finished and it took her several months to create it. She first copied it onto a tanned rabbit skin, that way she could carry it around as a portable reference.


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When the table was complete, she began to verify conclusions that she instinctively thought must be true. For example, as the tangent of an angle got smaller, so did the sine, but its cosine increased. On any given trigon, if you examined the small or "acute" angles, the sine of one would be equal to the cosine of the other and vise versa.

One day she came upon the most wonderful tree she had ever seen. It called to her. She climbed it up about fifty feet to where the bark was smooth. She decided to record all of her finding in this tree. She called it the "Tree of Mysteries".

Part 9: At age 11 Sophia's mom died. She was devastated.

Part 10: A few months later she met a boy named Targon in the woods. She was lonely and her loneliness overcome her fear of people. They became friends and he came back each day all summer. She wanted to share the stuff that had brought her so much pleasure all of her life, so she taught him how to write her secret symbols and how to add and subtract with them. She warned him not to say anything about this to anyone. He promised not to.

One day Targon's father made him mad so he told the man to shut up, because he, TARGON, was smarter. Targon showed his dad the symbols and the tribe ran out to the forest with knives and dogs ready to kill the evil that had infected their tribe.

Sophia escaped with only her life and the leather skin recording her trigon facts. She ran for what seemed like weeks. Finally she could run no more.

Part 11: At age 12 she was more lonely than ever. She knew it was time to select her grown name. She decided on a name that held the secret to all of her trigon findings in its spelling. Her sincere desire was that someday she would meet a person who would hear her name and understand the code. She would only be safe with someone who was able to understand her name.

She picked Soh-Cah-Toa.

  1. The capital "S" stood for SINE, the "o" and "h" for opposite to hypotenuse.
  2. The capital "C" stood for COSINE, the "a" and "h" for adjacent to hypotenuse.
  3. The capital "T" stood for TANGENT, the "o" and "a" for opposite to adjacent.

Part 12: Till age 15 Soh-Cah-Toa lived in a cave. She worked feverishly on her legacy. She carved and painted on the cave walls everything that she had learned from her earliest known explorations: her symbols, and how to count, add, subtract, multiply and divide with them, squares and square roots written in tables, her "Pythagorean Theorem" investigations, and mostly her beloved trigon relationships.

The legacy stretched across several rooms of the cave. She was careful to do her work deep inside the cave so that a casual explorer would not run across it by accident.

Part 13: At age 16 she could bear the loneliness no longer. This time she was much more wise about her approach. She knew she couldn't just walk in and say, "Hi, let's be friends." She secretly observed the village for about a month from a vantage point high up in a tree. She got to see some of the same people over and over. She even made up names for them.

The one who she thought might be approachable was a girl she saw every morning at the edge of the clearing, near the woods. Each day this girl would limp over to the berries growing there and pick a big basket full. It appeared that this girl must have one leg shorter than the other and that caused the rather pronounced limp. Soh-Cah-Toa also noticed that this girl was not included into the regular tribal activities. She seemed to spend most of her time working, but always by herself.

It was this girl who the great spirit told Soh-Cah-Toa to approach. She did and they developed a friendship quickly. The girl said her name was Grith, meaning "ugly one". Right away Soh-Cah-Toa said, "I won't call you that. Your name must be Mira, meaning "beautiful" for anyone can see that you have the beauty of the great spirit of life in your eyes."

Soh-Cah-Toa did not tell Mira about the mysteries for a very long time, but eventually she did let her see the cave and she shared a few of the basics. Mira knew to keep her mouth shut, and she did. The tribe never knew about Soh-Cah-Toa.

Part 14: At age 17 Soh-Cah-Toa looked up one morning to see Mira running at her top speed. She had the fear of death in her eyes. Mira and her little brother Sage had been climbing a tree, he fell and broke his leg. The bone had snapped and broken through his skin. When he saw the blood, he had screamed and then fallen into shock. Mira knew that the tribe would not allow her dear brother Sage to live. He was now infirm and would be put to the knife. She could only think of one thing to do. Go to Soh-Cah-Toa the wise one, and see if she could fix the leg.

Soh-Cah-Toa knew it was dangerous, but she had to help. They found the boy and brought him to the cave. There Soh-Cah-Toa set the bone and cleansed the wound like her mother had taught her. She then rigged a support brace out of strong branches in the shape of overlapping right trigons to hold the leg rigid. She wrapped the brace tight to his leg with damp reeds and told Mira that the bone would heal but it would take at least one full moon cycle before he could walk on it. The next day she sent them home and prepared for the worst.

Soh-Cah-Toa was still getting her things in order, preparing to leave, when she heard the dogs enter the cave. There was no escape this time. The people had found the "evil" and it would be destroyed. They grabbed her, took her back to the village, and killed her in front of everyone. It was just as Catherine had feared, her daughter expired at the hands of ignorant, violent, animals with knives yielded wildly and without mercy.

As she lay there dying, Soh-Cah-Toa melted into mind and spirit...

Her pain was to the point of unbearable. The last physically conscious thoughts that she willed her mind to make were for persons alive and yet to be born.

"....Dear great spirit of life and thought, let a piece of me live in the mental essence of all who follow me through the ages. I humbly beg you to let my existence make itself known in them with a feeling of such intense joy that it can only be described among those of kindred spirit and experience.

I beg of you to let them know at least a few moments of that which you have blessed me. The mental circle will be complete, if they can know a small piece....oh please, please, honor this my only request...."

She felt one last piercing of the knife at her legs. The pain was so intense in one last flash and then it was gone completely. Although her body lived a few hours more, Soh-Cah-Toa was at last free. Totally free as she had never been before in all of her seventeen years.

Epilogue: Two years later Mira went back to the cave and learned. She spent the rest of her life learning the mysteries left there by her friend Soh-Cah-Toa. Mira taught the basics of the mysteries to her babies by singing, and playing, and making trigons with them. As they grew she taught them more, in secret.

This learning was Mira's family secret, and it was passed on each generation. The secret learning went with them as they dispersed all over the world. Others eventually heard of it and claimed pieces of it as their own discoveries. So that now, the memory of Soh-Cah-Toa lives only in legend. But, is it true?

If you have ever known the joy of understanding a hard math concept after hours of deep struggle, or even days of work, the feeling of rapture that you got, when it finally "clicked" and you understood, is her essence, transcending time and touching your spirit even if only for a few seconds.

 

* We at themathlab.com BELIEVE!

 

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