Many years ago a carpet layer showed this puzzle to me. His question was whether the area a given piece of carpet covered was constant or not. I said, 'Of course'. He proceeded to tell me he could cut a 64 sf piece of carpet and cover 65 sf area. He was right or there would be no reason for this puzzle. The puzzler is, 'how did he do it'?
Hint, start with a piece of paper and draw an 8" by 8" square.
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Carpet Layer a Geometric Puzzler
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- stahrwe
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Re: Carpet Layer a Geometric Puzzler
Draw a line straight across the paper at 5"
You will now have two rectangles
a 5" by 8"
and
a 3" by 8"
You will now have two rectangles
a 5" by 8"
and
a 3" by 8"
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- Interbane
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- stahrwe
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Re: Carpet Layer a Geometric Puzzler
Divide the 3" by 8" rectangle into two equal right triangles.
There is one more step after this one and then you will cut apart the figures into four pieces which you will rearrange into a rectangle.
If you can figure out the final line to draw on the 5 by 8 rectangle post the endpoints otherwise I will provide the solution tomorrow.
There is one more step after this one and then you will cut apart the figures into four pieces which you will rearrange into a rectangle.
If you can figure out the final line to draw on the 5 by 8 rectangle post the endpoints otherwise I will provide the solution tomorrow.
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- stahrwe
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Re: Carpet Layer a Geometric Puzzler
Lay the 5 by 8 rectangle out and draw a diagonal from the 5 inch point to the 3 inch point on the long side.
Cut the rectangle into two pieces along the line.
Now take these pieces and the two right triangles and arrange them into a rectangle with sides 5 by 13
You started with a square 8 by 8 = 64 si
now you have a rectangle 8 by 13 = 65 si
How is that possible?
Cut the rectangle into two pieces along the line.
Now take these pieces and the two right triangles and arrange them into a rectangle with sides 5 by 13
You started with a square 8 by 8 = 64 si
now you have a rectangle 8 by 13 = 65 si
How is that possible?
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- johnson1010
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Re: Carpet Layer a Geometric Puzzler
the slopes of your cuts are not the same.
In the difference lies the area of the additional apparent square inch.
In the difference lies the area of the additional apparent square inch.
In the absence of God, I found Man.
-Guillermo Del Torro
Are you pushing your own short comings on us and safely hating them from a distance?
Is this the virtue of faith? To never change your mind: especially when you should?
Young Earth Creationists take offense at the idea that we have a common heritage with other animals. Why is being the descendant of a mud golem any better?
-Guillermo Del Torro
Are you pushing your own short comings on us and safely hating them from a distance?
Is this the virtue of faith? To never change your mind: especially when you should?
Young Earth Creationists take offense at the idea that we have a common heritage with other animals. Why is being the descendant of a mud golem any better?
- Interbane
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Re: Carpet Layer a Geometric Puzzler
The problem would become obvious if decimal points were included, I assume.
- stahrwe
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Re: Carpet Layer a Geometric Puzzler
Why didn't you post the slopes?johnson1010 wrote:the slopes of your cuts are not the same.
In the difference lies the area of the additional apparent square inch.
3/8
2/5
15/40
16/40
Did you get the point?
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- johnson1010
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Re: Carpet Layer a Geometric Puzzler
oh, sorry.
Thought maybe other people could check into it as well.
Yeah, i broke out my highly out of shape math skills.
Thought maybe other people could check into it as well.
Yeah, i broke out my highly out of shape math skills.
In the absence of God, I found Man.
-Guillermo Del Torro
Are you pushing your own short comings on us and safely hating them from a distance?
Is this the virtue of faith? To never change your mind: especially when you should?
Young Earth Creationists take offense at the idea that we have a common heritage with other animals. Why is being the descendant of a mud golem any better?
-Guillermo Del Torro
Are you pushing your own short comings on us and safely hating them from a distance?
Is this the virtue of faith? To never change your mind: especially when you should?
Young Earth Creationists take offense at the idea that we have a common heritage with other animals. Why is being the descendant of a mud golem any better?