Guess where is the missing square

[BobTheCrate]

Yep, I'm guilty as charged there F.G

I like to think of myself as a 'reluctant Windows user' though.

[The Lone Gunman]

Bob. I am not disputing your maths, though I do disagree. (I have looked at the diagram and see it as Integer measurements). I am assuming you have modified the lengths to fit your hypothetical proper triangle model, which BTW would affect all the angles and make the two sub triangle similar.

What I am asking you is how do you account for the empty square in the second figure?
You have clearly demonstrated an unshakeable knowledge of the area of each sub shape and the area of the master. You must agree that none of the shapes changes size in any way so the areas remain as constants.
How do you then explain the hole which is 1 square unit in the second figure which takes the total area of the second figure (allow me to round off here) 33.5 square units?

[Lucifer Box]

Aspergers, anyone?

Oooh, yes please. Lightly griddled with some olive oil and crushed sea salt. Just a twist of pepper thanks.

[BobTheCrate]

Lone Gunman,

Thank you for your words of praise not withstanding your understandable reservations regarding the newly formed triangle. After the endless barrage of stupid idiotic rantings from MotorMouth it makes a welcome change as I'm sure you might agree.

As I asked Fortune Green a while back. Would you mind dreadfully waiting for MotorMouth to catch up with the 1st triangle before we move onto the re-arranged one ? I don't think it productive anyone else gets embroiled in MotorMouth's deranged rantings. All will be explained to resolution once I can move onto the re-arranged triangle, I promise.

[BobTheCrate]

I don't dispute that your figures add up to 32.4999 but I find it funny that this does not match the area of the triangle.

I think most would agree you used many more superlatives than 'funny' to describe my calculations.
So now your endless ridiculing of my calculations is about a 0.0001 difference ? Is this what all your rantings amount to - a 0.0001 difference ?

Of that 0.0001 difference you said, just to recap :-

Your figures are obviously incorrect! LOL

For instance, please explain how you got the figure of 7.3845(?) for the area of the orange shape (other than subtracting your other calculations from 32.5 in an effort to make things add up)?

Using your (incorrect) measurements you have in fact shown that this shape has an area of 7. Doh!

You now conceed after a lot of prompting that my 4 areas do add up to 32.4999. That really you found it hilarious that 32.4999 did not match 32.50.

Hence

LOL hahahahahahahaha - when 'proving' your maths you could at least PRETEND it adds up!

and

Excellent.

I was referring DIMWIT to the fact that your excruciatingly pointless and anal calculations do not even add up to the area of the triangle.

and

As a rule mathematical 'proofs' don't involve statements like "the figures very nearly add up therefore we can assume they are correct".

So educate us Oliver. What is your explanation for that 0.0001 difference, or your best guess ?

Then we'll see if it matches my explanation.

And don't try to wriggle out of it by now trying to say you NOW meant all along the re-arranged triangle. We're talking about my geometrically true right angle triangle and you know it. We'll come onto the re-arranged one soon enough.

[The Lone Gunman]

I am happy to wait.

I think you should step back from this and re-evaluate your position.
You are never going to prove that the 4 sub units, whose areas are invariant, can possibly be manipulated in any way to fit in an area smaller than their sum.
Which is what you are proposing with diag 2 using your proposed proper triangle with a blank space.