Any mathematicians out there??

I considered asking my son, who lectures in mathematics at a university. However I don't expect I would understand his explanation, assuming he could answer, so I haven't bothered. When he was completing his PhD he sent me his thesis to read. Sadly the only bit that made sense to me was the acknowledgements! I know my limitations!

AN41

Build a straight fence across the middle and let the poor cow loose, else it'll have starved to death by the time we lot figure it out. 😉

It's ok, it's been rustled while we were trying to work it out.

Luckygirl3

NOW I remember why I hated maths at school! All so blooming pointless.

Just put a fence across to confine the cow to half the field!

Well, it's not pointless because we use Maths in some form or other every day.
However, perhaps some Maths is more relevant and useful than other Maths.
As I don't have a cow, this is not really elevant to me! 😂

Build a straight fence across the middle and let the poor cow loose, else it'll have starved to death by the time we lot figure it out. 😉

NOW I remember why I hated maths at school! All so blooming pointless.

Just put a fence across to confine the cow to half the field!

Katek

Oh that kind of grass.........

😂

Oh that kind of grass.........

Nibbles44

Goats can jump & climb & chew through ropes, so it must be a chain! Why would anyone have a circular field in the first place, or want it to eat only half the grass, or why they would want a crescent of grass left? Can't I simply move the stake to the middle of the circle & make the length of rope half the radius?

Has the cow metamorphosed into a goat?

Perhaps there was something in the grass. 🐄🐐

I can't remember much at all about any of the maths I was exposed to. At one time I could still prove with the appropriate diagrams that pythagoras theorem was true for any right-angled triangle, not just the easy 3-4-5 one and the other easy one (the sides of that now escape me, too, as well as the proof) I can still argue convincingly, given a long enough piece of string, that it is useful in the Real World if you are stranded on a desert island and want to build a house that doesn't have unsquare rooms.

Elegran

pen50 Sorry but I disagree with you. I think multiplying would work better than dividing, as the bit marked out by what the cow can reach while her tether is 35% of the diameter will be less than the 50% that she is supposed to be eating. I am trying to draw and post a diagram of what I mean but so far not succeeding.

I think you need to use sine because the area will be the same size as two segments of the circle. The area is relatively simple to calculate, but I can't remember much about trigonometry.

You and your brother need to find some other topics of conversation?!

Goats can jump & climb & chew through ropes, so it must be a chain! Why would anyone have a circular field in the first place, or want it to eat only half the grass, or why they would want a crescent of grass left? Can't I simply move the stake to the middle of the circle & make the length of rope half the radius?

Blinko

And the application in the real world is….?

There isn't one, Blinko It is purely to exercise the brain and keep it on its toes, just as going to the gym and doing repetitive movements has no application in the real world and is purely to exercise the body and keep it on its toes.

pen50 Sorry but I disagree with you. I think multiplying would work better than dividing, as the bit marked out by what the cow can reach while her tether is 35% of the diameter will be less than the 50% that she is supposed to be eating. I am trying to draw and post a diagram of what I mean but so far not succeeding.

And the application in the real world is….?

The rope should be one half of the diameter of the field divided by the square root of two - approximately 35% of the diameter.

Mogsmaw

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 am a hearty fan of education, but honestly, some of the things we were taught ! Yours is a good example.

Mine is as follows: the whole class sent out to the pavement in front of the school armed with the blackboard ruler and protractor to calculate the distance the sun is from the earth.

Now why would even a maths mistress feel that every one of a class of 24 girls would either as schoolgirls or as adults find a use for this piece of information?

And if we did need it, I never have, we could have found the answer in any encyclopedia!

I know of some cows that jumped over an electric fence and escaped.

Just erect an electric fence across the middle, use a compass to find the middle. It's easy when you don't know how

If he tethers them to stakes opposite each other on the edge of the field, they will each eat a half-circle from where they are tied. Then he can move both their tethers to points at right angles to their first points, so that they can each eat the uneaten grass in the bits outside the semicircles they were eating first.

Maybe he can charge the rightful owner of the second cow for the grass that it has eaten, and use the money to pay for all the extra stakes and rope he has had to buy, and to pay the labourer with a hammer who banged the stakes in.

He gets/borrows another cow. He tethers both to the stake in the middle of the circle of grass - and lets them sort it out. If they get their ropes tangled - then tough luck, they are after all imaginary cows.

It is very cruel to tether the cow, so if I call the RSPCA they will take it away. End of problem.

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 😀

I love your answer Grannynannywanny....

Buttercup says she's thoroughly fed up, lonely and needs to be milked.
🐄

It doesn't give the length of the rope, so it could be longer than the radius The exact half doesn't need to end at a straight line, it could be a curve. If it goes over the diameter line at the centre, it could compensate by not stretching as far as the line at the edges.