Where's Pythagoras when ya need 'im? A Puzzler

[JoBelle]

http://www.begent.freeserve.co.uk/triangle.htm

It's a fun one for you math types. 😉

 

[Dave2112]

If you count the squares, you're still covering the same area. Only the parts have been moved around.😎

 

[Haltickling]

Joby

I sucked at maths, so I asked my younger daughter who is a genius. Here's her reply: "The red triangle has a smaller ascendance than the green one. Therefore the red triangle in the first pic is minimally bent outward, while it's minimally bent inward in the second pic. That sums up to the small difference in surface."

I don't pretend to see that, so I simply ask you: Is this the correct answer? 😎

 

[amk714]

If you count the squares, you're still covering the same area. Only the parts have been moved around.😎

That's true, Dave, but both triangles are EXACTLY the same size and shape, yet one has a square "hole" in it, and the other doesn't! 😀

 

[amk714]

Re: Joby

I sucked at maths, so I asked my younger daughter who is a genius. Here's her reply: "The red triangle has a smaller ascendance than the green one. Therefore the red triangle in the first pic is minimally bent outward, while it's minimally bent inward in the second pic. That sums up to the small difference in surface."

I don't pretend to see that, so I simply ask you: Is this the correct answer? 😎

I don't think so, because both triangles are two-dimensional and are on a flat surface in the same plane. 😀

 

[amk714]

http://www.begent.freeserve.co.uk/triangle.htm

It's a fun one for you math types. 😉

Congrats, Joby. You've stumped a math major--ME! 😀

I'm working on the answer, so be patient. 😛

 

[amk714]

OK, I think I've got it. Without going into all the math I did and confusing everyone 😛, I've decided to put the short answer in silver font--if you give up, select the text and you'll see it! Here it is: The shapes AREN'T triangles! 😀

Good puzzle, Joby. Thanks for making me brush up on my math skills! 🙂

 

[ForgottenTcklr]

How does that answer it Amk.

I don't see that as an answer. It seems like an excuse for why you're not sure!

I think you do need to explain the math!

 

[amk714]

OK, FT, you asked for it, but be warned, it isn't pretty, especially since I don't have any math fonts! 😀

If these shapes form big triangles, then the length of the hypotenuse (longest side) = sqrt(5^2 + 13^2)= sqrt(194). But the sum of the lengths of the hypotenuses of the 2 smaller triangles = sqrt(2^2 + 5^2) + sqrt(3^2+8^2) = sqrt(29) + sqrt(73), which isn't equal to sqrt(194). So they aren't triangles, and that's why there's a hole in one of them! 🙂

There's more math I could post, but this is enough for starters. 😛

 

[ForgottenTcklr]

Okay Amk,

Now I follow you. I wasn't sure if you were serious, or just making a joke to prove an easier point!!!

 

[Haltickling]

clarification

I talked to my daughter again, because amk's equations puzzled me even more than the problem itself. She offered an easier explanation:

The long side of the overall triangle (hypotenuse) can't be a straight line, it shows a small, almost invisible crack.

Evidence:
The grade of ascension of the red triangle is 8 squares by 3 squares, while it's 5 by 2 squares in the green triangle.
8 : 3 = 2.6666....
5 : 2 = 2.5

Therefore it's not the same shape in both pictures, and hence nothing indicates that two different geometrical figures MUST have the same surface area.

Hey, even I understood that... 😛

 

[ForgottenTcklr]

Thanks Hal,

That is a lot easier to understand!!!

 

[Neutron]

Uh...

You're not talking Surface area. Surface area is 3 dimensional. This is a two dimensional figure/


Tron

 

[Neutron]

Dave is Absolutely Correct...

There is no real math proof for it, because you changed the basic shapes substance so you changed the assumptions.
It's comparing apples and oranges.

When you moved the red triangle to the top you forced everything to shift because you moved nothing else. The square left over is basically the area od the extra distance you had to move the base of the triangle in order for the whole figure to make a triagular shape. (NOTE not a true triangle)

Tron

 

[amk714]

Re: clarification

Evidence:
The grade of ascension of the red triangle is 8 squares by 3 squares, while it's 5 by 2 squares in the green triangle.
8 : 3 = 2.6666....
5 : 2 = 2.5

You're absolutely right, Hal. Sometimes we math majors get just a little too technical! 😛 Thank your daughter for me. 🙂

P.S. She seems pretty intelligent. If she's over 18, is she, um, available? 😀

 

[Haltickling]

Thanks, I'll pass it on, amk! But she's only 15, so keep your hands off her! 😀 My elder daughter is 20, but she's too busy studying pharmacology, so I didn't want to distract her. She's off-limits as well, I'm afraid, as she's in love with an engineering student. Both are very attractive and intelligent. I wonder whom they inherited it from... 😛

 

[ForgottenTcklr]

Hal,

You are a lucky man. You have two kids, both of which seemed to have turned out well. That's a great merit to yourself right there!!!