Another geometry puzzle

Stump your fellow simians.
ceptimus
Posts: 1437
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

Another geometry puzzle

Post by ceptimus »

Find the angle ϴ

triangle.png
ceptimus
Posts: 1437
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

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.
Witness
Posts: 35689
Joined: Thu Sep 19, 2013 5:50 pm

Re: Another geometry puzzle

Post by Witness »

30°.
Witness
Posts: 35689
Joined: Thu Sep 19, 2013 5:50 pm

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
ceptimus
Posts: 1437
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

Re: Another geometry puzzle

Post by ceptimus »

Here's the way I did it, just using basic geometry.
Spoiler:
My solution on the Freethought Forum from posted 14 years ago (but I worked it out a few years before then).
Spoiler:
The puzzle is a famous one posed in the Mathematical Gazette by Edward Mann Langley in 1922
Bruce
Posts: 20678
Joined: Wed Jun 09, 2004 11:46 pm
Title: Bruce of all Bruces
Location: Massachusetts

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! "
Witness
Posts: 35689
Joined: Thu Sep 19, 2013 5:50 pm

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:
Bruce
Posts: 20678
Joined: Wed Jun 09, 2004 11:46 pm
Title: Bruce of all Bruces
Location: Massachusetts

Re: Another geometry puzzle

Post by Bruce »

:figamagee:
gnome
Posts: 25947
Joined: Tue Jun 29, 2004 12:40 am
Location: New Port Richey, FL

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.
Witness
Posts: 35689
Joined: Thu Sep 19, 2013 5:50 pm

Re: Another geometry puzzle

Post by Witness »

↑ You mean like the probability of choosing any real number?
Bruce
Posts: 20678
Joined: Wed Jun 09, 2004 11:46 pm
Title: Bruce of all Bruces
Location: Massachusetts

Re: Another geometry puzzle

Post by Bruce »

:mrgreen: Perfect excuse to keep the whole pizza to myself.
Rob Lister
Posts: 23535
Joined: Sun Jul 18, 2004 7:15 pm
Title: Incipient toppler
Location: Swimming in Lake Ed

Re: Another geometry puzzle

Post by Rob Lister »

Zeno might submit that there is no way to provide 1/4th a slice.
ceptimus
Posts: 1437
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

Re: Another geometry puzzle

Post by ceptimus »

What's the volume of a circular pizza with radius z, and height a?
gnome
Posts: 25947
Joined: Tue Jun 29, 2004 12:40 am
Location: New Port Richey, FL

Re: Another geometry puzzle

Post by gnome »

V=πz2a
ceptimus
Posts: 1437
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

Re: Another geometry puzzle

Post by ceptimus »

Yes, or in plain ASCII, V = Pi z z a
Rob Lister
Posts: 23535
Joined: Sun Jul 18, 2004 7:15 pm
Title: Incipient toppler
Location: Swimming in Lake Ed

Re: Another geometry puzzle

Post by Rob Lister »

What is the most cost effective size of a pizza hut pizza.
gnome
Posts: 25947
Joined: Tue Jun 29, 2004 12:40 am
Location: New Port Richey, FL

Re: Another geometry puzzle

Post by gnome »

Without looking, almost always the largest size.
ceptimus
Posts: 1437
Joined: Wed Jun 02, 2004 11:04 pm
Location: UK

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.
Doctor X
Posts: 74877
Joined: Fri Jun 04, 2004 8:09 pm
Title: Collective Messiah
Location: Your Mom

Re: Another geometry puzzle

Post by Doctor X »



– J.D.