Any mathematicians out there??

Sorry, way beyond me! Hope someone solves this for you - there are some very clever people on GN !

I am not a mathematician, and would build a wall across the circle, going through the exact centre, and confine the cow in one half. However, the logic of the question goes something like this:-

The length of the rope (L) is the radius of the circle.
The area (A) of a circle is Pi R squared.
So half the area (B) of the circle is Pi R squared divided by 2.
What you need to find is B.

B = the square root of ( ( 3.14 x R ) divided by 2)

But maybe not.

Life’s too short!

No, I forgot to substitute the length of the rope (L) for (R) into the standard equation for finding the area of the circle.

Should be B = the square root of ( ( 3.14 x L ) divided by 2)
Or maybe not.

I'll send this puzzle to MY brother. He doesn't have enough to keep his brain exercised since he retired.

Now I have finished my coffee, I can see that my equation only gives you an area covered by a circle nearest the post which is clearly not as big as the area of the rest of the round field outside that circle.

I give up.

I remember this from school. The maths teacher concluded it was a problem for advanced mathematics and not something we could solve at school. I suspected then, as I do now, that he hadn’t the skills to solve it!

I googled this and still don’t understand the answer 😀

Whats it fer ??
🤣🤣🤣🤣🤣🤣🤣

This mathematical problem has been discussed for almost 300 years featuring tethered horses, cows, goats and caged birds.

www.quantamagazine.org/after-centuries-a-seemingly-simple-math-problem-gets-an-exact-solution-20201209/

You’ve got me stumped. I think I’d leave the cow in the adjoining field. Cut the grass on half the field, rake it up and throw it over the hedge 😀

Elegran

Now I have finished my coffee, I can see that my equation only gives you an area covered by a circle nearest the post which is clearly not as big as the area of the rest of the round field outside that circle.

I give up.

Yes, the first thing that struck me was the the cow is tethered to the edge of a circular field.

Logically
A) I've rarely seen a circular field
B) I've never seen a cow tied up in a field
C) The grass always looks greener on the other side of the fence so the cow might try to get through to another field.

My brain hurt just thinking about it.

Elegran

I'll send this puzzle to MY brother. He doesn't have enough to keep his brain exercised since he retired.

I'm not going to ask DH.
I could be there all day as he explains this, complete with diagrams - then asks me which farmer would be daft enough do this 🐄

My DH prides himself on his mathematical knowledge (and indeed has taught some maths in years gone by) and loves such puzzles. He has spent an hour on it so far with no luck and has gone to do something else. Never known this before!

For myself, I USED to be a wizard at Maths and got a Grade 1 in my O-level at age 14. I too am stumped, but not yet giving up!

I'm now reliably informed that there's advanced calculus used in this..........😱😱

A chum of mine had a goat tied to a stake hammered into the ground just near enough to the fence that the stupid creature (the goat, not my friend - or maybe...) jumped over and hanged itself on the rope over the fence.

Your task is to calculate the statistical odds of that happening...

The formula for the area of a semi circle is; πr2/2

Grannynannywanny

You’ve got me stumped. I think I’d leave the cow in the adjoining field. Cut the grass on half the field, rake it up and throw it over the hedge 😀

Aaargh! Calculus!

I got as far as working out that you need to first calculate the area of the semi-circle, as mentioned by M0nica, then find out how to calculate the size of an oval that had the same area as the semi-circle ie. half the area of the circle. (The curve of the oval must fit into the circle and leave a negative space in the shape of a crescent that has the same area as the semi-circle) Then measure the diameter at the widest point to give the length of the rope. I did not have a clue how to do all this so I went off and got on with some gardening.

M0nica

The formula for the area of a semi circle is; πr2/2

Yes, but that is a semicircle with the non-semicircular edge flat. This one has the "other" edge as part of the circumference of the circular field, therefore it has two curved edges, neither of them defined by their radii, so there are (at least) two unknowns in the equation (or equations, as I suspect we have to do more than one operation)

If the farmer puts the cow into the barn and waits until the grass has turned into hay, he could feed half of it to the cow. Meanwhile it can eat silage from last year's grass crop, made more exciting by potato peelings and apple cores from the farm kitchen.

Get a smaller field