I read an article in the AMTI’s 2015 publication of ‘The Mathematics Teacher’ titled ‘Trigonometry- History and Pedagogy’ by Mr. E. Krishnan. I found two very interesting stories in it. Both in the life of Thales, the Greek scholar.
The first incident:
One day, Thales was summoned by the king, who asked him to measure the distance of the ship anchored far in the sea. Thales set about doing the job. He positioned a pole at the edge of the shore, such that it was in line with the anchored ship. Then he planted another pole at the edge of the shore such that both the poles were in a straight line.
Next, he put a third pole in the exact middle position to the first and second poles. Finally, he positioned himself in a place such that the the third pole and the ship are exactly one behind the other. So, it looked like this.
Now, the problem is solved! The ship, the first pole, and the third pole form a right angled triangle that is congruent to the the right-angled triangle formed by Thales, the second pole and the third pole. So, if he wants to know the distance of the ship in the sea, all he has to do now is measure the distance between him and the second pole! Amazing, right?
The second incident:
When Thales was experimenting, he found the height of of the Egyptian pyramid by comparing the shadows of the pyramid and his staff! Well, he used similar triangles property. But, where are the similar triangles?
He planted his staff perpendicular to the base of one side of the pyramid. Since, it is the shadow that he is comparing(from the light from the sun), it formed the same angles. So, the ratios of the shadows of the pyramid to the staff is the same as the height of the pyramid to the staff. He knew the height of the shadows, and his staff. So, boom! He got the height of the pyramid! Clever, right?
I loved these two stories. The article was very nice!
It was a good read.
(Note: The diagrams featured above are mine.)