Last night I went to the crest movie theater the only movie theater in Seattle that offers $4 movie tickets. Entering the theater my sister nudged me to” live a little ” the problem is I strictly hold myself to a diet, and when I break the diet in my head I’m thinking ” I already broke my diet so to hell with it ” I bought a large soda, a large popcorn and a one-pound bag of candy. What a disaster🤬😖 …. at least Incredibles 2 was fun and entertaining.
Today’s inspiration for my blog post came from staring at my bookshelf
Sacred Mathematics: Japanese Temple Geometry
I’d like to share two mathematical puzzles The first being The puzzle of the missing dollar. The second a Sagaku Geometrical problem proposed by a 13-year old Japanese kid the Pythagoras theorem is all that is needed to solve this one. I’m sure over the course of your life someone has shown you an argument that purportedly shows that 1=0 but if you look closely you can usually find the error.I greatly enjoy catching these subtle errors and I hope it’s something you might enjoy as well ….Or at least I hope you enjoy reading. Now at the risk of being called mean-spirited, I will not leave The solutions. I hope you enjoy trying to figure it out by yourself
The missing dollar
Three friends walk into a hotel to rent a room the clerk charges them $30 so they each pay $10 and hand it to the clerk. Now on the way back to his desk the clerk realizes that he has overcharged. He was only supposed to charge them $25 so to rectify the situation he takes $5 and gives it to the Bellboy and tells the Bellboy to return the $5 to these three friends now the Bellboy on his way over thinks himself “hey these pals don’t know that they have been overcharged so what I’m going to do is take $2 out of the five and put it in my pocket as a tip and hand $3 to the friends ” so he hands the $3 back to them and they split amongst themselves . however, if you think about it each friend has now paid $9 to the hotel and the Bellboy pocketed $2 and if you add everything up 9 + 9+ 9 + 2 =29
So the question is where did the missing dollar go?
Now before I present to you the second problem I’d like to share with you the history behind Sangaku which I found interesting.
During the Edo period, 1603 -1868 Japanese rulers enforced a strict cultural isolation between Japan and the Western World which means there had very little communication between them. One of the most interesting practices that came out as a result of this isolation is the practice of sangaku
learned poeple of all classes ,from farmers to samurai, produced theorems in Euclidean geometry. These theorems appeared as beautifully colored drawings on wooden tablets which were hung under one of the roof in the precincts of a shrine or temple.
The tablet was called a SANGAKU which means a mathematics tablet in Japanese. Many skilled geometers dedicated a SANGAKU in order to thank the god for the discovery of a theorem. The proof of the proposed theorem was rarely given. This was interpreted as a challenge to other geometers, “See if you can prove this.”
the text was copied from here
when people discovered an interesting geometrical math problem they found so insightful that they Associated it with a spiritual value. they would carve it onto a wooden tablet and leave it as an offering at their local shrine.
Below are three sizes of circle: two black, three white, one grey. Four of the circles are inscribed inside a square which together with the other circles is inscribed inside a triangle. Show that the radius of the grey circle is twice that of the black circles.
The Solutions won’t be found on this post, but if you would like to know the solutions
you can find them by googling The Missing dollar
and the 3-4-5 triangle by a kid