Discussion
Moonhawk said:
TwigtheWonderkid said:
In hindsight, there was nothing wrong with the modern method, it was just different, not worse.
Yep - loads of different ways to achieve the same thing - all give the correct answer.I quite like the Japanese way of doing multiplication - very easy and visual method.
It's a really good visualisation, almost one you can hold in your head - I utubed a few of these and I think with a wavey line for a zero and a zig zag line for fives it works really well.
I've taken a few brief looks for a division method and found this.
Every day is a school day - brilliant stuff!
Right from day one I was always telling Little Ex that 9+4 is the same as 10+3, 3x9 is the same as 3x10 minus 3x1, 8x4 is the same as 4x10 minus 4x2 - and minus 8 is take ten add two... you get the drift.
As RobM77 said - Calculus really isn't that difficult in method - the issue is understanding what numbers you have and what you need to do to them to get the answer you want - that is the clever bit.
I remember when trigonometry finally PROPERLY clicked with me, angles, circles, triangles, SIN, COS, TAN, Pythagoras, all these in the back of your mind meaning you can jump in your mind from an angle and length into the other side of the triangle, then you can easily apply a bit of calculus, and then suddenly you are understanding phase and amplitude and learning all about Radio, TV and Satellite communications, Phase Shift Keying and Amplitude Modulation, Constellation Diagrams.
I might not be able to work the actual real numbers, but I understand exactly what they relate to. PAL for example - that's the transmission system used to put a picture on your TV - it stands for Phase Alternate Lines, a very clever system.
@groundcontrol - I know you asked for numerical reasoning, but numerical reasoning just seems to be 'sums' you know adding, subtracting, multiplying.
My old man is a Prof in physiology & cardiology, and I cannot calculate the maths he is using for sheer stress in the arterial wall, in fact the mathematicians at his University cannot come up with a model either!
He has the recorded data, he wanted a mathematical formula (Fourier Transformations) to describe what is happening but they can't find one! (Climate change anyone?).
But, when starting a new year with the freshers his first statement in the first lecture is always along the lines of "You might not graduate with a first after this set of lectures, you might not know everything there is to know - but I guarantee you'll be able to talk one to one with your GP".
Great thread - let's keep it alive.
Maths is ace!
Fonz said:
Moonhawk said:
I quite like the Japanese way of doing multiplication - very easy and visual method.
Could someone please explain this to me as I'm just not getting it. :You then divide the diamond shape into columns and add up all of the intersections in each column.
https://www.youtube.com/watch?v=_AJvshZmYPs
Edited by Moonhawk on Wednesday 30th September 16:13
I'm not getting it. If the crocodile's faster in water it should swim diagonally until exactly adjacent to the zebra, then head out for Mr Lunch at right angles. If it's faster on land it should head for the bank at right angles and then leg it along the bank.
Presumably there is no current and Mr Lunch doesn't move.
So I make 't' 20 metres plus the small extra bit caused by it having to cross the river. So how wide is the river...?
Presumably there is no current and Mr Lunch doesn't move.
So I make 't' 20 metres plus the small extra bit caused by it having to cross the river. So how wide is the river...?
Simpo Two said:
So how wide is the river...?
In Scotland that'll be uni level 
The formula as given takes that into account as you can see, and as a result it specifies T as a function of x only.
This is necessary as you will appreciate so that students can miss a chance to use the chain rule.
Simpo Two said:
I'm not getting it. If the crocodile's faster in water it should swim diagonally until exactly adjacent to the zebra, then head out for Mr Lunch at right angles. If it's faster on land it should head for the bank at right angles and then leg it along the bank.
Presumably there is no current and Mr Lunch doesn't move.
So I make 't' 20 metres plus the small extra bit caused by it having to cross the river. So how wide is the river...?
It would be good if there was some sort of way of working out the answer to this, with maths or something.Presumably there is no current and Mr Lunch doesn't move.
So I make 't' 20 metres plus the small extra bit caused by it having to cross the river. So how wide is the river...?
TheInternet said:
Simpo Two said:
I'm not getting it. If the crocodile's faster in water it should swim diagonally until exactly adjacent to the zebra, then head out for Mr Lunch at right angles. If it's faster on land it should head for the bank at right angles and then leg it along the bank.
Presumably there is no current and Mr Lunch doesn't move.
So I make 't' 20 metres plus the small extra bit caused by it having to cross the river. So how wide is the river...?
It would be good if there was some sort of way of working out the answer to this, with maths or something.Presumably there is no current and Mr Lunch doesn't move.
So I make 't' 20 metres plus the small extra bit caused by it having to cross the river. So how wide is the river...?
turbobloke said:
This (below) was too hard for students taking a maths exam in Scotland. Presumably the kerfuffle was over the last part if the question not the simple calculations but even so ye gods.
What exactly was the issue with this question? Identifying the problem, or the difficulty of maths involved in solving it?TheInternet said:
turbobloke said:
This (below) was too hard for students taking a maths exam in Scotland. Presumably the kerfuffle was over the last part if the question not the simple calculations but even so ye gods.
What exactly was the issue with this question? Identifying the problem, or the difficulty of maths involved in solving it?turbobloke said:
Simpo Two said:
So how wide is the river...?
The formula as given takes that into account as you can see...TheInternet said:
It would be good if there was some sort of way of working out the answer to this, with maths or something.
Speaking as an idiot, I see it as essentially a right-angled triangle. One side is 20m, you just need another side - here the distance between croc and bank. Is the croc on the opposite side of the river? Looks like there's a bit more bank there to cross... is the diagram to scale? How far is the lunch from the bank?For A i) solve the equation where x = 20 (the prey is 20m away and he swims all of it. Therefore the point he meets the opposite bank is 20m downstream)
For A ii) solve the equation where x = 0 (he swims the least amount of distance, which is directly to the other bank. so 0m downstream.)
Looking at the equation you can see why either of these two extremes are not ideal; basically Mr Croc's time taken on land is 4(20-x) and his time taken in water is 5*sqrt(36+x^2)
There's a happy medium in there somewhere
For A ii) solve the equation where x = 0 (he swims the least amount of distance, which is directly to the other bank. so 0m downstream.)
Looking at the equation you can see why either of these two extremes are not ideal; basically Mr Croc's time taken on land is 4(20-x) and his time taken in water is 5*sqrt(36+x^2)
There's a happy medium in there somewhere
Edited by a7x88 on Saturday 10th October 21:57
As said, chain rules.
The river is 36 m wide, but you don't need to know that.
The minimum time is when the function T(x) is a minimum, i.e. dT/dx = 0
Differentiate T = 5 (36 + x^2)^(1/2) + 4(30 - x) wrt x
gives
5x/(36 + x^2)^(1/2) - 4 = 0
so
5x/(36 + x^2)^(1/2) = 4
25x^2 = 16(36 + x^2)
9x^2 = 576
x = 8
T(8) = 98 tenths = 9.8 seconds
The river is 36 m wide, but you don't need to know that.
The minimum time is when the function T(x) is a minimum, i.e. dT/dx = 0
Differentiate T = 5 (36 + x^2)^(1/2) + 4(30 - x) wrt x
gives
5x/(36 + x^2)^(1/2) - 4 = 0
so
5x/(36 + x^2)^(1/2) = 4
25x^2 = 16(36 + x^2)
9x^2 = 576
x = 8
T(8) = 98 tenths = 9.8 seconds
Edited by V8LM on Saturday 10th October 21:54
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