I enjoyed your example. When I was a student, these types of stories made the math more relatable. I remember these apocryphal stories; I doubt their authenticity but found them amusing.
- Pythagoras was part of what we would call a religious cult. They were trying to discover the secret of the universe when they stumbled on PI and the Pythagorean theorem.
- The Sumerians counted in sixes. From them, we have sixty seconds in a minute, sixty minutes in an hour. Don't know why a day only has 24 hours. Maybe the royal mathematician goofed up and got sacrificed to Tiamat.
- Today, we count in tens. But you see artifacts of counting by twenty in our language. Lincoln's Gettysburg address begins with Four score and seven years ago our fathers brought forth, upon this continent, a new nation. Four score means four twenties or eighty.
- Trigonometry was created by enterprising Greek merchants who had fleets of ships. One problem they had was determining how far a ship was from port. They solved the problem by creating a virtual right triangle. On shore, they marked a "shore line" which they would place two observers. The two observers always stood on the line and at a known distance from one another by means of a fixed rope. The first observer would walk up and down the line. The second observer would adjust his position on the line to keep the same distance from the first. The first observer would walk up and down the line until he thought he was "perpendicular" to the ship which was at sea. The second observer would then write down the estimated angle between the shoreline and the ship. By knowing this angle (theta), the fixed distance between observers (adjacent distance), and the right/90 degree angle... they could calculate the distance to the ship (opposite distance). In other words, the distance to the ship is equal to the tangent of theta multiplied by the adjacent distance.