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>> No. 4877 Anonymous
20th February 2021
Saturday 9:29 pm
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Did you know this? The Pythagorean theorem is a special case when c = d. I just realised this.
Expand all images.
>> No. 4878 Anonymous
20th February 2021
Saturday 10:13 pm
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When c squared equals d squared, then a squared also b squared, and that means that a square you have there fella.
>> No. 4879 Anonymous
20th February 2021
Saturday 10:43 pm
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>>4878
Thicko.
>> No. 4880 Anonymous
21st February 2021
Sunday 5:54 pm
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This is a parallelogram, right? c and d don't look equal from the diagram.
>> No. 4881 Anonymous
21st February 2021
Sunday 6:01 pm
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Pythagoras, the man who used to talk to bears and claimed to have a golden thigh and be son of the god Apollo? And had a magic arrow he used to fly? Why should I believe anything he says?
>> No. 4883 Anonymous
21st February 2021
Sunday 6:13 pm
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>>4880
c and d can be anything, the diagram is just to show you where they are not how big they are.
>> No. 4886 Anonymous
21st February 2021
Sunday 7:15 pm
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>>4883

But c and d can only be equal when the parallelogram is, in fact, a square. In which case they are both the hypotenuses to a right angled triangle in which each opposite and adjacent is equal to the length of the side of a square.
>> No. 4887 Anonymous
21st February 2021
Sunday 7:19 pm
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>>4886
What about fucking rectangles.
>> No. 4888 Anonymous
21st February 2021
Sunday 8:55 pm
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>>4887
Then it is no longer a right-angle and this theorem no longer applies.
>> No. 4889 Anonymous
21st February 2021
Sunday 9:13 pm
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>>4888
But c and d are equal.
>> No. 4890 Anonymous
21st February 2021
Sunday 9:33 pm
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>>4886
Exactly the point of >>4878
>> No. 4891 Anonymous
21st February 2021
Sunday 10:12 pm
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>>4889
>>4890
The only rectangle this could work in is a square. Any rectangle with non-equal side lengths cannot be filled with four right-angled triangles.
>> No. 4892 Anonymous
22nd February 2021
Monday 1:22 am
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>>4891
Who cares about that? I'm just saying c and d can be equal in a rectangle, not just a square.
>> No. 4893 Anonymous
22nd February 2021
Monday 10:36 am
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>>4892
Okay, so? Are you being deliberately obtuse (pun intended) or do you not understand that unless it's in a square they can't be perpendicular and so won't form right-angled triangles?

Given that in >>4889 you seemed to think that c and d being equal made it still hold up I'm going for the latter, and hence you should care about my 'proof' in >>4891 because it demonstrates that this will only work in a square.
>> No. 4894 Anonymous
22nd February 2021
Monday 11:39 am
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>>4893
> But c and d can only be equal when the parallelogram is, in fact, a square.
This. This is the only thing I'm critiqueing. I'm not interested in any theorums or right-angles or anything.
>> No. 4895 Anonymous
22nd February 2021
Monday 11:55 am
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Just admit you fucked up OP. I'm not looking into the maths too hard but how difficult is it when you're saying c = d to post an illustration where c actually does = d?
>> No. 4896 Anonymous
22nd February 2021
Monday 12:28 pm
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>>4893
So now to actually get into your codswallop: When c==d, we have a rectangle. Lets say a = 3 and b = 4 and plug that into OP's formula. What do we get? c==5 and d==5.
>> No. 4897 Anonymous
22nd February 2021
Monday 2:42 pm
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>>4896
OP's image is predicated on the angle between C and D being 90º.

C is 2.5, not 5.

If a ≠ b and c = d then it must be a non-square rectangle. Therefore if you are not using a square, the angle between c and d cannot be 90º. In fact, none of the angles in the triangle are 90º.

If there is no 90º angle, then the Pythagorean theorem does not apply, and the formula cannot be applied.
>> No. 4898 Anonymous
22nd February 2021
Monday 2:57 pm
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>>4897
Pythagoras is just a special case of al-Kashi where the cosine term is zero. In the situation in the OP, the cosine terms cancel.
>> No. 4899 Anonymous
22nd February 2021
Monday 5:09 pm
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c = a + b
d = a - b

c^2 = a^2 + b^2 + 2a.b
d^2 = a^2 + b^2 - 2a.b

The +2a.b and -2a.b cancel each other out so it works for any angle. Isn't that pretty?
>> No. 4900 Anonymous
22nd February 2021
Monday 5:21 pm
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>>4897
Rectangles have right-angles.
>> No. 4901 Anonymous
22nd February 2021
Monday 5:50 pm
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>>4897
If a = WY and b = YZ, then c = WZ, not OZ.

WYZ is the right angle that gives you Python Gonorrhoea or whatever.
>> No. 4902 Anonymous
22nd February 2021
Monday 6:02 pm
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>>4900
The angles in rectangles are usually right ones, except in Savile-Epstein rectangles, where they're wrong ones.
>> No. 4903 Anonymous
22nd February 2021
Monday 8:32 pm
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>> No. 4904 Anonymous
23rd February 2021
Tuesday 3:57 pm
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>>4903

The sum of the squares on the diagonals is equal to the sum of the squares on the perimeter.
>> No. 4905 Anonymous
23rd February 2021
Tuesday 5:02 pm
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Why not use a ruler?
>> No. 4906 Anonymous
23rd February 2021
Tuesday 5:03 pm
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>>4905
The Greeks were a democracy.
>> No. 4907 Anonymous
23rd February 2021
Tuesday 5:05 pm
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>>4906
You've done it now, the antiquarians will be all over you for this one.
>> No. 4908 Anonymous
23rd February 2021
Tuesday 6:52 pm
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>>4907
The great thing is that next time people say "republic, not democracy" you can point out that the two are effectively translations of each other.

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