Mathematics Q&A

CJ
Rank 12
Joined: December 3rd, 2009, 10:33 am

April 29th, 2018, 9:45 am #1

Okay - so, first of all, I started a topic like this on The Lightweb - and, I thought, "Perhaps TCH could also do with a topic of a similar nature that never gets used :lol: !

Secondly, I'm a First Class Mathematics graduate, with a Master's degree from St John's College, Oxford. It's been a major part of my life, so rather than simply shutting up about it as though it's something I should be ashamed of, I thought I should open up a place where I can discuss it.

They can be about a specific area of mathematics, or about the subject as a whole. They can be about basic maths you learned at school, all the way up to university level (though, I'm not really qualified to answer anything about PhD-level and beyond :P ). They don't even have to include any mathematics: they can be non-mathematical questions about the process of studying mathematics, or what makes mathematicians tick.

I'll be happy to answer a maths problem or two (especially 'fun' ones); however, I don't want this to turn into a place where I do people's homework for them. That's a waste of my time which doesn't help anybody to become a better mathematician. So, for example, I'm not going to answer questions like this:
wrote:What is the derivative of sin(x)?
However, if you can show that you've made a serious effort to solve the problem yourself, then I'll be more than happy to provide hints to help you progress. So, for example, if you ask me the following:
wrote:I need to find out what the derivative of sin(x) is. I know from the definition of a 'derivative' that it's the limit (as h -> 0) of [sin(x+h) - sin(x)]/h, but now I'm stuck :( . Can you help me?
Then, I'll gladly give you a hint :) . I'll point you to the trigonometric identity "sin(x + h) = sin(x)cos(h) + cos(x)sin(h)", and suggest substituting that in.

So, ask away :D . (Or, if you hate mathematics, then just move on to the next thread - but I'm guessing you've already long since done that by now :P )
Last edited by CJ on May 4th, 2018, 5:53 pm, edited 4 times in total.
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JHG
Rank 9
Joined: March 14th, 2016, 9:10 pm

April 29th, 2018, 4:05 pm #2

According to the square/cube law, what would a person the size of a Tyrannosaurus rex weigh?
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5819
Rank 7
Joined: July 6th, 2017, 9:30 pm

April 29th, 2018, 6:38 pm #3

What's your favorite number?
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CJ
Rank 12
Joined: December 3rd, 2009, 10:33 am

April 29th, 2018, 6:43 pm #4

JHG wrote:According to the square/cube law, what would a person the size of a Tyrannosaurus rex weigh?
You did read my opening post in full, didn't you? Including the part where I said I don't answer maths problems here :P ?
5819 wrote:What's your favorite number?
5820. Just as a bit of gratuitous one-upmanship :lol:
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5819
Rank 7
Joined: July 6th, 2017, 9:30 pm

May 4th, 2018, 4:55 pm #5

Is it impossible to divide a pie into equal thirds?
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CJ
Rank 12
Joined: December 3rd, 2009, 10:33 am

May 4th, 2018, 5:06 pm #6

If you have the kitchen equivalent of a straight-edge and compass, then you can construct 120-degree angles - which gives you all you need to divide a pie into three :) .
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JHG
Rank 9
Joined: March 14th, 2016, 9:10 pm

May 4th, 2018, 5:31 pm #7

How much would a Tyrannosaurus rex weigh if it's height were shrunk to that of a Borrower?
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CJ
Rank 12
Joined: December 3rd, 2009, 10:33 am

May 4th, 2018, 5:52 pm #8

Okay, I'll modify what I said in the opening post. I'll answer 'fun' questions like these, but I reserve the right not to answer questions from somebody if I get the sense that they're trying to get me to do their homework for them.

So, the weight of a T. rex. Their height could be anything up to around 6m, and their weight could be anything up to around 9,000kg. So, let's use a big, heavy one :P .

Meanwhile, a Borrower is 10cm (or 0.1m) tall. That is, a Borrower is 0.1/6 = 1/60 of the height of our T.rex. Now, the weight of the T. rex is proportional to its volume - so, reducing it to 1/60 of its normal height would reduce it to 1/603 = 1/216,000 of its normal weight. So, its weight would be:

9,000/216,000 = 0.0417 kg = 41.7 grams (to 1 decimal place).

Not a very intimidating T. rex :( !
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5819
Rank 7
Joined: July 6th, 2017, 9:30 pm

May 5th, 2018, 5:39 am #9

CJ wrote:If you have the kitchen equivalent of a straight-edge and compass, then you can construct 120-degree angles - which gives you all you need to divide a pie into three :) .
Ah, but 100% divided by 3 is... well it doesn't divide evenly. You just get 33.3333333%

So what about that 0.0000001%?

Doesn't that make 4 pieces, but one is extremely small?
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Pyrite
Rank 9
Joined: December 24th, 2009, 12:53 pm

May 5th, 2018, 6:31 am #10

5819 wrote:
CJ wrote:If you have the kitchen equivalent of a straight-edge and compass, then you can construct 120-degree angles - which gives you all you need to divide a pie into three :) .
Ah, but 100% divided by 3 is... well it doesn't divide evenly. You just get 33.3333333%

So what about that 0.0000001%?

Doesn't that make 4 pieces, but one is extremely small?
No, it's not just 33.33333333%, because the 3 is recurring. So it is 33.3333333333333...%, where the 3's continue on to infinity. In other words, if you add those three together, you get to 100%.

It's the same reason why 9/9 is 0.999999999... and also 1.
Last edited by Pyrite on May 5th, 2018, 6:32 am, edited 1 time in total.
CJ wrote:Also, you can solve walls faster than [Donald Trump] can build them.
So there's that.
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