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Q&A #6237

Teachers' Lounge Discussion: Trigonometry

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2002022418:06:07
Subject: Re: Pythagorean's Property

You can use the Pythagorean Property to show that it applies to
squares and circles as well as triangles.  for example, the area of a
3 inch circle and a 4 inch circle will have the same area as a 5 inch
circle. A 3 inch water pipe and a 4 inch water pipe will exactly fill
a 5 inch water pipe where all three are equal length.   

You can make mobiles to hang from the ceiling that are based upon the
subject property also.  For example, you can hang a three inch circle
and a 4 inch circle equal distant from a point and hang a 5 inch
circle the same distance from the point and the mobile will be
balanced.

If it is warm, you can take the students outside, using lime for
making lines, and demonstrate how to make a large rectangle the size
of a house and using the property to make a corner exactly 90 degrees.
If you don't want to use the familiar 3,4 5 or 6, 8, 10 triangle, you
can use some of the following. 
 a        b       c
6612	115	6613
1624	57	1625
760	39	761
420	29	421
264	23	265
180	19	181
1196	147	1205
920	129	929
1435	228	1453
525	92	533
476	93	485
357	76	365
1209	280	1241
1600	399	1649
1380	371	1429
1080	329	1129
391	120	409
176	57	185
35	12	37
140	51	149
352	135	377
925	372	997
2301	980	2501
520	231	569
77	36	85
80	39	89
589	300	661
15	8	17
72	65	97
460	429	629
924	893	1285
697	696	985

Check out the last one, it is almost a perfect square.

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