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If time permits, a nice ending for the presentation is to share the story of the Babylonian tablet and Dr. Super's Trigram Puzzle. Here is the story in capsule form. Embellish as appropriate.
Before developing Dr. Super's Triangles for Creative Publications, Dr. Behrouz Aghevli (pronounced Bay rooz' Ah gav' lee) actually discovered (invented) a Tangram like puzzle using 1 large, 3 medium and 5 small triangles in what is now the Dr. Super's Triangle set. The discovery of that puzzle, which he calls the Trigram puzzle, came when Dr. Aghevli was trying to divide an equilateral triangle into 5 congruent right triangles.
Dr. Aghevli was aware of and fascinated by the reported 4000 year old history of the traditional 7 piece Tangram puzzle. As the story goes, the Emperor Tan had a square mosaic tile in his possession. One day, while strolling in the garden, Tan dropped the tile and it broke into seven pieces. You guessed it!! Those seven pieces are the familiar and famous seven Tangram pieces. And, it was reported that Tan spent hours and hours trying to rearrange those seven pieces into the original square, hence the origin of the famous Tangram puzzle.
While FINDING the tale intriguing, Dr. Aghevli believes that the reported story of the origin of the Tangram puzzle, circulated in the early 1900s by several well known English puzzle writers, is "phoney baloney," as they say.
Anyway, early in their working relationship (during the summer of 1991), Dr. Aghevli showed his Trigram puzzle to his collaborator and co-developer of the Dr. Super's Triangle materials, Dr. Mark Spikell, a professor at George Mason University in Fairfax, VA. And, in a spirit of comedic interplay, when Dr. Spikell inquired about the origin of the Trigram puzzle, Dr. Aghevli wove a fairly tall tale about discovering the puzzle on an ancient, 4000 year old Persian tablet that had been in his family for centuries. Dr. Aghevli was, of course, "pulling Professor Spikell's leg," so to speak, and had no such tablet in his possession.
Unknown to Dr. Aghevli at the time, Professor Spikell never actually believed the tale and proceeded to humor his colleague by allowing him to think he believed the tale he had been told.
On Christmas day of the same year, Dr. Aghevli was showing a friend his newly developed Trigram puzzle. A few days later, the friend called Dr. Aghevli and said they had to meet for lunch to discuss a very urgent matter. He would not reveal the nature of the meeting.
At the meeting, the friend told Dr. Aghevli he had quite a surprise for him. He handed Dr. Aghevli a physical replica of an ancient tablet he had seen in a museum in Baghdad, Iraq, many years before. The friend had been so captivated by the actual tablet that he purchased a replica, to bring back to the United States.
Show the picture of the original tablet in the museum in Iraq. Direct the participants attention to the triangular shape at the top of the tablet.
Yes, you guessed it again. The triangles pictured look very much like the triangles in the Dr. Super's Triangles set.!!!!!!
You may point out that a large, a medium and a small triangle fit on the tablet almost perfectly.
It is truly an understatement to say that both Dr. Aghevli and Dr. Spikell were very surprised to learn of the existence of such a tablet containing the Dr. Super's Trigram Puzzle pieces. They were literally incredulous. And, Dr. Aghevli began the academic journey into the history of mathematics to track down the real truth and story of the tablet.
Here is what Dr. Aghevli learned.
Scholars in the Babylonian culture and language, informed Dr. Aghevli that the tablet is believed to be one of the first mathematical problem texts from the Old Babylonian era. The triangles pictured are not actually the 306090 triangles in Dr. Super's set, though they surely "appear" to be of those angle measurements. Actually, it turns out that the triangles are 345 right triangles, a fact apparently made clear when the text on the tablet is translated.
Interestingly, it is believed that this tablet represents one of the first known demonstrations of the very famous theorem attributed to the Greek mathematician, Pythagorus, a theorem learned (or memorized) by virtually all school children. The theorem states that in a right triangle, a2 + b2 = c2 , where a and b are the lengths of the legs and c is the length of the hypotenuse. And, if true, this Babylonian demonstration of Pythagorus' theorem would have preceded the work of Pythagorus by some 1300 years.
Through his research on this tablet, Dr. Aghevli learned a great deal about the contributions of the Babylonians in mathematics. And, as a result, he and Professor Spikell included in the book, Dr. Super's Triangles: Fraction Explorations, the interesting Babylonian accordion that is made with a folded rectangle the size of 60 small triangles. The accordion can be used to show all the important fractions: 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/20, 1/30 and 1/60.
Note: This is an ideal opportunity to introduce any number of topics from the history of mathematics. Teachers could use the story about the tablet to motivate a discussion of the valuable contributions to mathematics of various civilizations and cultures, not just the Babylonians.
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