Rabbit chase

Dr.Peterson said:
Yes, I knew that the answer is simple in the case of 4 chasers, but didn't want to take to time to work out the n=3 case.

en.wikipedia.org

Mice problem - Wikipedia

en.wikipedia.org en.wikipedia.org

It looks like they didn't pay attention to the difference.
Click to expand...
Does Wikipedia has a typo?

It says that time [imath]\displaystyle = \frac{1}{1-\cos\frac{2\pi}{n}}[/imath] when actually this is the distance!

blamocur said:
I posted this problem because the answer in the book is wrong :

View attachment 38664
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Is the correct answer:

[imath]\displaystyle d_{3} = \frac{1}{1-\cos\frac{2\pi}{3}} = \frac{2}{3}[/imath]

?

Of course this distance is based on a unit side, so with a side of [imath]100[/imath] yards, the distance should be:

[imath]\displaystyle d = \frac{2}{3}100 = \frac{200}{3} \approx 66.67 \ \text{yards}[/imath]
 
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mario99 said:
Does Wikipedia has a typo?

It says that time [imath]\displaystyle = \frac{1}{1-\cos\frac{2\pi}{n}}[/imath] when actually this is the distance!
Click to expand...
Did you fail to read carefully what they said?

The most common version has the mice starting at the corners of a unit square, moving at unit speed.​

So time and distance are equivalent in their formulation. In one unit of time, they move one unit of distance.
 
Dr.Peterson said:
Did you fail to read carefully what they said?

The most common version has the mice starting at the corners of a unit square, moving at unit speed.​

So time and distance are equivalent in their formulation. In one unit of time, they move one unit of distance.
Click to expand...
You are right.

🤦‍♂️
 
mario99 said:
Does Wikipedia has a typo?

It says that time [imath]\displaystyle = \frac{1}{1-\cos\frac{2\pi}{n}}[/imath] when actually this is the distance!


Is the correct answer:

[imath]\displaystyle d_{3} = \frac{1}{1-\cos\frac{2\pi}{3}} = \frac{2}{3}[/imath]

?

Of course this distance is based on a unit side, so with a side of [imath]100[/imath] yards, the distance should be:

[imath]\displaystyle d = \frac{2}{3}100 = \frac{200}{3} \approx 66.67 \ \text{yards}[/imath]
Click to expand...

The book, published in 1971, predates Wikipedia by three decades :) I got 2/3 for the answer too.
 
lookagain said:
Does Wikipedia have a typo?
Click to expand...
You are awesome professor lookagain. Thanks a lot for correcting my grammar. My cat has jumped on my keyboard and distracted me for 1 second while I was about to write "have", then my brain saw Wikipedia and wrote "has" automatically.

Cats should be caged!

🐈🐈‍⬛
 
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