I definitely get the gist I looked at what you sent period there's also one would a chocolate bar if you cut it a certain way after eating one piece you can make the entire bar again.. that's what I thought what you posted was akin to because I was going to actually say maybe the missing Square is borrowing a slight amount of area from each box..in other words if you had a undetectable stripe of one color edging all the other colors to make it vanish

There's an easy way to see that the lower figure contains an extra square cm.

In both cases, the entire colored figure is drawn on a 5 x 13 cm rectangle of area 65 sq cm.

If you work out the blank area OUTSIDE the first colored figure, you get 12 + 5 + 16 = 33 sq cm, so the figure itself must contain 65 - 33 = 32 sq cm.

Doing the same for the outside of the lower colored figure, you get 12 + 5 + 15 = 32 sq cm, so the figure itself must contain 65 - 32 = 33 sq cm, one more than in the first case.

The lower figure contains exactly the same amount of blue, red, green, and purple areas, it is just taking up more space because the colored areas were moved and one squares worth of uncolored space is now located inside the colored area, instead of outside.

Yes, that happens because the (entire) colored area is not a true triangle in either case. The slope of the green triangle is a little steeper than that of the red one.

It is a packing problem. In the first case, the 32 colored squares pack together perfectly with no gaps to form the upper pseudo-triangle; In the second, the 32 colored squares pack together with one blank square left over. That's the 33rd square of the lower pseudo-triangle.

You didn't?
Gee, you only needed simple arithmetic to follow my solution. Just addition, subtraction and multiplication of integers.

The link's proof was so complicated, Thomas even had to leave out steps, in the interests of "sparing you the arithmetic" of adding and subtracting quantities raised to the fourth power and then taking the square root of the result, but I guess you did all that in your head.

The why of the illusion was obvious from the beginning... the colored pseudo-triangle can't be a real triangle. The vertical and horizontal sides are straight, so the hypotenuse must be bent.

I'm talking about proving that the extra blank area is exactly 1 sq cm. The link used a sledge hammer to crack a peanut.

I once had an algebra teacher that told us not to make problems more complicated than they needed to be. That was wise advice then, and remains so today.

Were it obvious to everyone, it wouldn't be a paradox, now would it?

I agree with your teacher and that the link went further into the math than was necessary. Your original statement, however, was an oversimplification that still didn't explain the paradox to those it was not obvious to.

There are easily-resolved momentary paradoxes (like this "triangle" illusion) and there are also difficult paradoxes (such as those posed by quantum mechanics) that even the world's greatest physicists have not yet been able to resolve after 100 years.

Here is an old paradox, akin in some ways to the "triangle."

Three traveling salesmen, in order to save money, agree to share a room at a cheap hotel. The desk clerk tells them the overnight rate for the room is $30, and collects $10 from each salesman.

A short time later, the clerk realizes he made a mistake, that he should only have charged $25 for the particular room he gave the salesmen.

So the clerk gives the bellhop $5 in singles and sends him to the room with instructions to give the $5 to the salesmen.

But the bellhop is dishonest, giving only $3 to the salesmen ($1 to each), and keeping $2 for himself.

Now comes the question: Each salesman made a net payment of $9, or $27 total. The bellhop has $2. What happened to the remaining dollar of the original $30?

The Omnipotent Paradox dates back to the 12th century to Averroës who asked, “Could an omnipotent being create a stone so heavy that even they could not lift it?” This would be like seeking an answer to the question, “What would happen if an irresistible force were to meet an immovable object?” This statement seems to make sense at first, but upon closer examination, we must ask if there is a force that is irresistible, and if there was, then there can be no immovable object. Both cannot be true because if an irresistible force does exist, then there cannot be an immovable object. The point is an object cannot in principle be immovable if a force exists that can in principle move it.

The answer is NO He cannot "do" that. Note that there is no limit however to the size of a rock that He can create, and there is no limit to the size of a rock that He can lift. Thus the question - answered in the negative - involves no limitation on God's prerogatives; if answered in the positive however does. The whole thing is a play on words.

Jokingly the point is we don't know if God has a limit to his own powers. When youman Ben's say he can do anything it might just pertain to what we consider anything no?

Can you fold an object that is unfoldable?

Well I would believe that its atoms can be considered folded in layers no?

Maybe...

Mash potato you can't fold mash it just makes a big f-ing mess. 乂^◡^乂

Way to go, ADA! Ha!

Ada science. 乂º◡^乂

Why would he want to?

I'll ask him that for you when I'm dead

Can something be sliced so thin it only has one side?

The youth of the sixties tried so hard to change the world

Why are they now trying so hard to change it back?

The answers you seek my dear are in University

Please explain.

Cause they all live in northern CA? :)

This puppet is false

I guess the answer depends on if he goes to the gym a lot

I really have nothing more to say on the matter thank you very much

This one's a killer hon. .. what did you get for an answer?

Ya up on your geometry, hon?

https://peterjamesthomas.com/tag/paradox/

I definitely get the gist I looked at what you sent period there's also one would a chocolate bar if you cut it a certain way after eating one piece you can make the entire bar again.. that's what I thought what you posted was akin to because I was going to actually say maybe the missing Square is borrowing a slight amount of area from each box..in other words if you had a undetectable stripe of one color edging all the other colors to make it vanish

There's an easy way to see that the lower figure contains an extra square cm.

In both cases, the entire colored figure is drawn on a 5 x 13 cm rectangle of area 65 sq cm.

If you work out the blank area OUTSIDE the first colored figure, you get 12 + 5 + 16 = 33 sq cm, so the figure itself must contain 65 - 33 = 32 sq cm.

Doing the same for the outside of the lower colored figure, you get 12 + 5 + 15 = 32 sq cm, so the figure itself must contain 65 - 32 = 33 sq cm, one more than in the first case.

The lower figure contains exactly the same amount of blue, red, green, and purple areas, it is just taking up more space because the colored areas were moved and one squares worth of uncolored space is now located inside the colored area, instead of outside.

Yes, that happens because the (entire) colored area is not a true triangle in either case. The slope of the green triangle is a little steeper than that of the red one.

It is a packing problem. In the first case, the 32 colored squares pack together perfectly with no gaps to form the upper pseudo-triangle; In the second, the 32 colored squares pack together with one blank square left over. That's the 33rd square of the lower pseudo-triangle.

I know why it is tbat wau, even supplied a link explaining it.

Sure, but the link then proceeded to show that the extra area was 1 sq cm by a needlessy complicated calculation.

Whatwver, Thinkerbell. It was an accurate explanation.

Ploddingly accurate? Yes.

Elegantly simple? No.

I am sorry, Thinkerbell, but I didn't find your explanation "elegantly simple". Have a nice night.

You didn't?

Gee, you only needed simple arithmetic to follow my solution. Just addition, subtraction and multiplication of integers.

The link's proof was so complicated, Thomas even had to leave out steps, in the interests of "sparing you the arithmetic" of adding and subtracting quantities raised to the fourth power and then taking the square root of the result, but I guess you did all that in your head.

Simply counting the squares does not explain the

whyof the illusion.The why of the illusion was obvious from the beginning... the colored pseudo-triangle can't be a real triangle. The vertical and horizontal sides are straight, so the hypotenuse must be bent.

I'm talking about proving that the extra blank area is exactly 1 sq cm. The link used a sledge hammer to crack a peanut.

I once had an algebra teacher that told us not to make problems more complicated than they needed to be. That was wise advice then, and remains so today.

Were it obvious to everyone, it wouldn't be a paradox, now would it?

I agree with your teacher and that the link went further into the math than was necessary. Your original statement, however, was an oversimplification that still didn't explain the paradox to those it was not obvious to.

Have a nice weekend, Thinkerbell.

There are easily-resolved momentary paradoxes (like this "triangle" illusion) and there are also difficult paradoxes (such as those posed by quantum mechanics) that even the world's greatest physicists have not yet been able to resolve after 100 years.

Here is an old paradox, akin in some ways to the "triangle."

Three traveling salesmen, in order to save money, agree to share a room at a cheap hotel. The desk clerk tells them the overnight rate for the room is $30, and collects $10 from each salesman.

A short time later, the clerk realizes he made a mistake, that he should only have charged $25 for the particular room he gave the salesmen.

So the clerk gives the bellhop $5 in singles and sends him to the room with instructions to give the $5 to the salesmen.

But the bellhop is dishonest, giving only $3 to the salesmen ($1 to each), and keeping $2 for himself.

Now comes the question: Each salesman made a net payment of $9, or $27 total. The bellhop has $2. What happened to the remaining dollar of the original $30?

The Omnipotent Paradox dates back to the 12th century to Averroës who asked, “Could an omnipotent being create a stone so heavy that even they could not lift it?” This would be like seeking an answer to the question, “What would happen if an irresistible force were to meet an immovable object?” This statement seems to make sense at first, but upon closer examination, we must ask if there is a force that is irresistible, and if there was, then there can be no immovable object. Both cannot be true because if an irresistible force does exist, then there cannot be an immovable object. The point is an object cannot in principle be immovable if a force exists that can in principle move it.

The answer is NO He cannot "do" that. Note that there is no limit however to the size of a rock that He can create, and there is no limit to the size of a rock that He can lift. Thus the question - answered in the negative - involves no limitation on God's prerogatives; if answered in the positive however does. The whole thing is a play on words.

Yes but God could add material to the Rock and limit himself to how much material he can lift without wearing a safety harness

What's your point Surf?

Jokingly the point is we don't know if God has a limit to his own powers. When youman Ben's say he can do anything it might just pertain to what we consider anything no?

A joking point?

Youdon't know about the power of God.I don't know youman Ben or what he has said.

That was a talk text error but let's stop beating this dead horse

OK, let's.

Surf, Your disbelief is not a license to berate others for their belief.

You don't take God seriously; I understand.

I do - understand?

This statement is false.

Was a question, i believe

No, but he did need a rest on the 7th day after the creation........

Can God make everybody believe in him if God doesn't exist?

You beat me to that one!

I usually do. :) :)

That's just silly. The bible mentions several things God can't do. For instance, He can't lie and He can't change.

God doesn't exist