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October 19th, 2008, 12:09 PM   #1
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Geometry problem

Here´s the problem: what is the lenght of de diagonal DH.
See image>>
Strangley by doing it wrong i get the correct answer!
Hope someone can tell me more.
Thanks,
jonathan
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October 19th, 2008, 12:29 PM   #2
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Re: Geometry problem

Think of a box bounded and defined by A, B, H, D and E. The rest is a red herring [there, and true, but extraneous.] DH is simply the body diagonal of that box: sqrt(4^2 + 2^2 + 3^2).
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October 19th, 2008, 03:31 PM   #3
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I don't undertand your calculation of DG, as DG = 5 by Pythagoras's theorem.
I don't understand why you say the angle G is not a right angle, as it is a right angle.
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October 20th, 2008, 03:17 AM   #4
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Re: Geometry problem

wow! Thanks guys ! I understand it now, it seems very simple, by just seeing a different shape inside the box! I was making it too dificult.
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October 20th, 2008, 06:39 AM   #5
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Re: Geometry problem

You might make it more interesting by finding angle HCD [which is not 90].
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October 21st, 2008, 01:13 PM   #6
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Re: Geometry problem

hmm,, i will have to think about how to do that... sure you will now someway, or do i have to work on the problem?
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October 22nd, 2008, 12:33 AM   #7
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Finding that angle requires use of trigonometry as well as geometry.
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October 22nd, 2008, 06:32 AM   #8
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Quote:
Originally Posted by skipjack
Finding that angle requires use of trigonometry as well as geometry.
Of course, the triangle having sides of sqrt(5), 2sqrt(5) and sqrt(29). I'm suggesting only that a person can learn more by stopping now and then and turning over a few rocks than by dashing madly through the forest. ...a personal philosophy I used when teaching, and that I think would improve the present educational system, if only slightly, there being so many other problems. It also points out that a seemingly difficult problem was in fact easy to solve, but a seemingly innocent one might not be as simple, and that the process of solution sometimes reveals properties of figures not otherwise noticed. I found this true many [many!] years back when solving the problem of three intersecting unit circles. They intersect in one common point and three others. The problem was to show that the three others lay on a unit circle. However, the real interest began when I saw wheels within wheels within that same structure.
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October 22nd, 2008, 09:23 AM   #9
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Re: Geometry problem

so there is more in mathematics than only logic... the use of imagination an intuition?
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October 22nd, 2008, 03:57 PM   #10
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Re: Geometry problem

Quote:
Originally Posted by jonathan
so there is more in mathematics than only logic... the use of imagination an intuition?
That is in everything, and includes also "insight'. It's a blend of experience, latent ability, and several other factors. Some simply can see what others can not. Some see far more than I ever will, to be sure. Thinks of something else, like music. Anyone can hit the black and white keys. Some can make music, either from reading the written notes on a page, or, very specially, by their own invention. Some can hit the keys better than others, the one, but not the other making music from exactly the same notes.
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