Another geometry puzzle

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ceptimus
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Another geometry puzzle

Post by ceptimus »

Find the angle ϴ

triangle.png
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ceptimus
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Re: Another geometry puzzle

Post by ceptimus »

Abdul Alhazred wrote: Mon Sep 28, 2020 9:47 pm Aren't the big one and the little one similar triangles?

I'll go with that == 20 degrees.
Spoiler:
I drew it accurately, so you can see that answer is wrong by measuring it on your screen with a protractor. The challenge, though, is to prove the value of theta using geometry or trigonometry.

It can be done with basic high school geometry - no special knowledge needed. But, of course, it's not obvious at first how to tackle it - which is what makes it an interesting puzzle. :)

It can also be done with high school trigonometry - but it can get a bit messy just using sines, cosines and tangents.

There's also probably a reasonably neat way to do it using basic trigonometry and simultaneous equations.
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Witness
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Re: Another geometry puzzle

Post by Witness »

30°.
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Re: Another geometry puzzle

Post by Witness »

Abdul Alhazred wrote: Wed Sep 30, 2020 12:41 pm How did you get there?
https://en.wikipedia.org/wiki/Law_of_sines
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ceptimus
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Re: Another geometry puzzle

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Re: Another geometry puzzle

Post by Bruce »

Brucetta requested 1/4 slice of pizza. Bruce gives her 1/3 slice of pizza. Brucetta says that's too much. What fraction of pizza will Bruce have to remove from the 1/3 slice of pizza to leave her with 1/4?

Bonus questions! How long will it take for Bruce and Mrs. Bruce to argue over the best means solve this puzzle? How long will the argument last before Brucetta says, "Forget about it! I'll just eat the whole 1/3! "
Such potential!
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Re: Another geometry puzzle

Post by Witness »

Bruce wrote: Sun Nov 22, 2020 5:50 pm Brucetta requested 1/4 slice of pizza. Bruce gives her 1/3 slice of pizza. Brucetta says that's too much. What fraction of pizza will Bruce have to remove from the 1/3 slice of pizza to leave her with 1/4?
1/12. You're joking, right? :notsure:
Bruce wrote: Sun Nov 22, 2020 5:50 pm Bonus questions! How long will it take for Bruce and Mrs. Bruce to argue over the best means solve this puzzle? How long will the argument last before Brucetta says, "Forget about it! I'll just eat the whole 1/3! "
Till late into the night, especially after lights out.

Brucetta will behave for 30 seconds (standard case) to 1 minute (on a good day).

Did I win? :mrgreen:
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Re: Another geometry puzzle

Post by Bruce »

:figamagee:
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Re: Another geometry puzzle

Post by gnome »

Witness wrote: Sun Nov 22, 2020 7:29 pm
Bruce wrote: Sun Nov 22, 2020 5:50 pm Brucetta requested 1/4 slice of pizza. Bruce gives her 1/3 slice of pizza. Brucetta says that's too much. What fraction of pizza will Bruce have to remove from the 1/3 slice of pizza to leave her with 1/4?
1/12. You're joking, right? :notsure:
Trick question. Regardless of the amount chosen, it will either be too much removed or too little removed.

In fact, it can be mathematically proven in R2 that the odds of slicing it at exactly the correct mark is literally zero.
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Re: Another geometry puzzle

Post by Witness »

↑ You mean like the probability of choosing any real number?
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Re: Another geometry puzzle

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:mrgreen: Perfect excuse to keep the whole pizza to myself.
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Re: Another geometry puzzle

Post by Rob Lister »

Zeno might submit that there is no way to provide 1/4th a slice.
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ceptimus
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Re: Another geometry puzzle

Post by ceptimus »

What's the volume of a circular pizza with radius z, and height a?
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Re: Another geometry puzzle

Post by gnome »

V=πz2a
"If fighting is sure to result in victory, then you must fight! Sun Tzu said that, and I'd say he knows a little bit more about fighting than you do, pal, because he invented it, and then he perfected it so that no living man could best him in the ring of honor. Then, he used his fight money to buy two of every animal on earth, and then he herded them onto a boat, and then he beat the crap out of every single one. And from that day forward any time a bunch of animals are together in one place it's called a zoo! (Beat) Unless it's a farm!"
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ceptimus
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Re: Another geometry puzzle

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Yes, or in plain ASCII, V = Pi z z a
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Re: Another geometry puzzle

Post by Rob Lister »

What is the most cost effective size of a pizza hut pizza.
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Re: Another geometry puzzle

Post by gnome »

Without looking, almost always the largest size.
"If fighting is sure to result in victory, then you must fight! Sun Tzu said that, and I'd say he knows a little bit more about fighting than you do, pal, because he invented it, and then he perfected it so that no living man could best him in the ring of honor. Then, he used his fight money to buy two of every animal on earth, and then he herded them onto a boat, and then he beat the crap out of every single one. And from that day forward any time a bunch of animals are together in one place it's called a zoo! (Beat) Unless it's a farm!"
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ceptimus
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Re: Another geometry puzzle

Post by ceptimus »

I would say the zero-size pizza hut pizza (i.e. don't buy one from there) is the most cost-effective solution. Instead, buy one from a supermarket and warm it up yourself.
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Re: Another geometry puzzle

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