The Maths Thread

[Plays By Sense Of Smell]

Another good one is the Monty Hall problem.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to swap to door No. 2?"

Should you switch? And why?

Always switch

 

[Stoned Rose]

It's estimated that for every 10 people, 1 person will understand binary, and 1 won't.

Not if they’re one of these ‘non-binary’ types they wont.

 

[In the Kippax]

How many 128ths in an inch?

3251.2?

 

[TheRemainsOfTheDave]

Can’t be bothered to check out the formulae, but pretty sure it’s something like working out the area of the circle so that you can then use half of the area to reverse calculate the radius for this new number?

Ok...and then I saw the ‘tethered at the edge’ bit’...so, trusting my in my roughshod heuristics...
Some kind of inverse degree calc based upon the initial distance from the stake that was calculated...as you may tell I was drunk when I started and am miles down the road now...

The solution for this type of problem is a lot simpler when you realise what needs to be done. Imagine a circle that is cut into 8 equal slices (like a pizza). We know the circle's area using π, so each slice is an eighth of that. The slice is not a triangle, but has a curved edge, so if we cut off the curved bit from the two ends of the curve we get a triangle and a segment (a bit like a Terry's chocolate orange wedge). If we calculate the area of the triangle, using the cosine function, and deduct that from the area of the slice, that's the area of the segment. If you put two of these segments together (straight edge to straight edge) you get the same shape (of the union) that you get when two circles overlap.

 

[Paladin]

The solution for this type of problem is a lot simpler when you realise what needs to be done. Imagine a circle that is cut into 8 equal slices (like a pizza). We know the circle's area using π, so each slice is an eighth of that. The slice is not a triangle, but has a curved edge, so if we cut off the curved bit from the two ends of the curve we get a triangle and a segment (a bit like a Terry's chocolate orange wedge). If we calculate the area of the triangle, using the cosine function, and deduct that from the area of the slice, that's the area of the segment. If you put two of these segments together (straight edge to straight edge) you get the same shape (of the union) that you get when two circles overlap.

Understood. But these two circles are of different diameters, so the overlapping shape is not symmetrical on both axes.

 

[TheRemainsOfTheDave]

Understood. But these two circles are of different diameters, so the overlapping shape is not symmetrical on both axes.

That's true, but the straight edges of segments are the same length so it works.

 

[Paladin]

My wife bought my son a tee shirt with a picture of Father Christmas and the text HO3, with the 3 in superscript text. We had a discussion yesterday whether the formula was correct or not.

Both me and my elder son thought the formula should be HO3, [or possibly (HO)3, 3(HO), 3HO]. My son, who is in year 2 studying maths at MMU said we could drop the brackets as the H and O were a single entity because each letter did not have a given distinct meaning or value. Fair enough.

He also argued that the formula was correct. We said it wasn't because it meant HO cubed, which wouldn't necessarily result in HO being said three times. He argued that didn't matter because HO was not a numerical expression.

All a bit confusing for me. Anyone able to shed any light on this? This picture shows the formula, but the model isn't my son, and it isn't the exact same shirt.

 

[worsleyweb]

Here’s a maths question - find a number between 10 and 99.

Reverse the digits and then divide your new number by 3 and it will be exactly 3 less than the number you started with.

What number did you start with?

 

[117 M34]

My wife bought my son a tee shirt with a picture of Father Christmas and the text HO3, with the 3 in superscript text. We had a discussion yesterday whether the formula was correct or not.

Both me and my elder son thought the formula should be HO3, [or possibly (HO)3, 3(HO), 3HO]. My son, who is in year 2 studying maths at MMU said we could drop the brackets as the H and O were a single entity because each letter did not have a given distinct meaning or value. Fair enough.

He also argued that the formula was correct. We said it wasn't because it meant HO cubed, which wouldn't necessarily result in HO being said three times. He argued that didn't matter because HO was not a numerical expression.

All a bit confusing for me. Anyone able to shed any light on this? This picture shows the formula, but the model isn't my son, and it isn't the exact same shirt.

I'd be inclined to agree with your son.
Ho isn't a number nor does it have a numerical value.
If we take the word Ho as one word (and apply a numerical value to it of 1 as it is one word) then it would be correct as 1 cubed is 3.

 

[Tuearts right boot]

My dad always used to ask me....how many beans make five.