The Home Machinist!

If you start with the large triangle as a single piece, you'll never reproduce the puzzle since smaller triangles sliced from the large one will have the same slope. The puzzle depends on the fact that the angles of the two smaller triangles are different. Given that fact, with their bases parallel, their hypotenuses can never form a continuous straight line.

I had hoped that when I pointed out the different slopes, folks would detect what was going on. I was wrong.

The real question is why ctwo is torturing us with this when we are clearly too stupid to figure it out.

I am sure you are familiar with misery loves company...

Here's one that's a bit simpler - no geometry, just simple algebra. It's a 'proof' that all the integers are equal to zero !

a = b
a² = ab
a² + a² = a² + ab
2a² = a² + ab
2a² - 2ab = a² + ab - 2ab
2a² - 2ab = a² - ab
2(a² - ab) = 1(a² - ab)
2 = 1

Now, if we subtract '1' from both sides, we have:

2 - 1 = 1 - 1
1 = 0

So, 0 = 1 = 2

Adding '1' we have:

1 + 1 = 2 + 1
2 = 3

We can continue adding '1' to both sides to prove that all the integers are equal to zero.

So, what's wrong here?

In the top series of equations, you multiplied by zero!

Let's see.

4(0) = 10(0)
4=10

Well done, Steve.

Technically, the problem is not MULTIPLYING by zero, which is legal.

4(0) = 10(0)

simply reduces to:

0 = 0

which is a tautology. It's when you DIVIDE by zero, an illegal operation, that you open up the possibility of "proving" almost anything.

This bit here is equivalent to my "proof," which I plan to submit for consideration for a Fields Medal.

2(a² - ab) = 1(a² - ab)
2 = 1

This is as old as the hills. It appears to be triangle but one side is ever so slightly concave to rob one unit square.

tornitore45 wrote: ↑Fri Nov 24, 2017 3:23 pm This is as old as the hills. It appears to be triangle but one side is ever so slightly concave to rob one unit square.

Probably that is old but I previously have never met it. We often solve short quizzes on the breaks at the college. Some of those in the thread are interesting to me. I gonna share with my friends, wanna make them confused

> I wanted to machine it out of aluminum, but I think I will not be able to pull off a good enough illusion.

I think it depends on the edges being a little ragged. Machine it carefully out of metal and the lines will almost disappear in the assembly on the left while there will be glaring gaps in the assembly on the right. Maybe if you mill it with one of those DIY drill-press conversions?

Now let's see a Banach-Tarski sphere dissection done in Delrin. Or maybe with a piece of fruit.

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

The pieces are not in the same arrangement Note that the two step pieces in the first image make a solid rectangle. Then the height of that rectangle is less that what is being perceived in the second arrangement. To make the triangles line up switch them. This makes the smaller triangle's height match the height of the two step pieces. The base of the larger triangle will match the width of the two adjacent step pieces.