11-07-2002, 12:27 PM | #11 | |
Apophis
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11-07-2002, 12:28 PM | #12 |
40th Level Warrior
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I just confirmed the theory by printing it out and cutting it in half and laying the drawings over top one another. There is an almost imperceptable slope change on the hypotenuse that creates a very thin convex sliver about 8 squares long - making up the missing square. Quite cool. Any teachers on this board? - show it to math students.
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11-07-2002, 12:31 PM | #13 | |
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11-07-2002, 12:32 PM | #14 | |
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11-07-2002, 12:37 PM | #15 | |
Xanathar Thieves Guild
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11-07-2002, 12:37 PM | #16 | |
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11-07-2002, 12:37 PM | #17 | |
Apophis
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[ 11-07-2002, 12:37 PM: Message edited by: WillowIX ] |
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11-07-2002, 12:38 PM | #18 |
Lord Ao
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Actually the triangle bit is a red herring. All three triangles are similar (angles equal, sides proportional), and the total area of the reconfigured large triangle is the same in each case.
The "hole" is created by the differeces in area of the two rectangles that make the difference in the large triangle when the two small triangles are lined up. With the small triangle on top, the resulting rectangle is 3x5, which has an area of 15. With the med triangle on top, the resulting rectangle is 2x8, which has an area of 16. So, when using discreate parts as shown in the picture, there is not enough material to complete the triange in the second configuration, even though the total area is the same for each large triangle.
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11-07-2002, 01:20 PM | #19 | |
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As for me having free time at work, we all obviously do. But, I've gotten several projects off my desk today, including pleadings in 2 cases, and I intend to finish up a bunch of discovery to pound the other side into the dirt by the time the day is finished. For young lawyers, a lot of the day is spent awaiting feedback on projects - I take work home at night most days. 'SNAP' *breaks arm patting self on back* |
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11-07-2002, 02:12 PM | #20 | |||
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Red triange is 3*8, green is 2*5. They are not similar, the gradient of the hypotenuse is different, rearranging them therefore allows for this gap to be created. This can bee seen, if you look at the point where the triablges meet in the first picture. IF your eyesight is super human, you can see a slight angle there. For the rest of us, look at the same point in the second diagram. The hypotenuse of the red triangle passes close to this point, not through it.
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