Math Is Fun Forum

Any luck? Free Wii points would be useful. O.o

In case my solution wasn't clear, I created a video;

http://www.youtube.com/watch?v=tSuD5a6rf38 (the example used is the problem you gave me)

If you need a bit of a re-cap on Pythagoras' Theorem, you might want to see my other video;

http://www.youtube.com/watch?v=vS_fbzvPtmU

I will also be creating sine, cosine and tangent videos, where I'll show in detail how to find angles and sides in right-angled triangles using sine, cosine and tangent. I'll also move on to 3-D trigonometry if you're interested, which is more of a GCSE topic.

EDIT: I have just created another video on the sine rule. You can see it here;

http://www.youtube.com/watch?v=DWKpQ4l94v8

It contains two examples of problems that I made up. I will include harder examples later, and more videos using the cosine and tangent rules, along with the inverse trig functions.

PS: Sorry for the terrible handwriting, I had to use a mouse.

Sometimes questions like that can be hard to imagine, so imagine in our rectangular solid we want to find the diagonal on the bottom of the solid. To do that, we need the length and the width (8 and 4) - by Pythagoras' Theorem, a² + b² = c²;

8² + 4² = c²
80 = c²
Square rooting both sides;
√80 = c

At this point, don't calculate that square root - you'll need the most precise possible value in order to complete the problem. Now that we have the diagonal that runs along the bottom, we can use that to find the diagonal that connects the two opposite corners in the rectangular solid that you are referring to. Here's why they gave us the height - 2. We use Pythagoras' Theorem again;

a² + b² = c²

2² + √80² = d²
4 + 80 = 84 (because the square root of something squared means they'll cancel out !)
d = √84

So the solution to the problem is that the diagonal is √84. If this is hard to picture in your head (which it is usually for most people without paper) then I can provide a video if need be.

Hi guys,

A Wacom Tablet might be a good idea... but quite expensive! In order to save money, my plan is to use a webcam (or some sort of video recording device) to film a sheet of paper that I'll be writing on in a standard felt-tip pen, whilst verbally giving explanations. People that do this are Allen Lin, Edugratis.com, and PatrickJMT (youtube.com/patrickjmt), who recently was the subject of an article. Tutoring is on the rise, and what makes it really easy to do is that it is relatively low-risk! The only costs would be transport and advertising costs, which aren't too expensive anyway (advertising a small business via poster usually only costs around 80p a week). And Easter is coming up, which is always the most popular time for tutoring.

I wonder if I could use Microsoft Mike.

He gave us the answer... but I'm still not convinced that it's unsolvable.

I believe anything that I think has enough evidence to be believed in, hence my love for physics - but by that statement, you could say that I should believe in theories of a 'God'; but the presence of a God would cause many questions to surface... and one of those questions would be questioning the purpose of life. But do things need a purpose? And, if one were to know one's purpose of living, would one's lifestyle change as a result?

I approve of anything that gives someone hope, but I disapprove of anyone's statement that states that their belief is wholly true. That's why it's a belief.

...and twenty-thousand years later, when code-breakers are anxiously awaiting the final permutation of Bob Farey's code, it is cracked. The message reads:

rofl i juts wast3d ur ti3m lols!!!!!!!!11

If I recall correctly his information was also based on Simon Singh - but the best source would be someone who was actually alive at the time.

@Bob Farey - is this your code?

So we know that you use a 26-letter wheel with letters arranged in a random (by a human or a computer - what method was used to pick the numbers?) order, and that the order in which the letters are read could be significant. Solvable by a computer? Eventually, yes. Solvable by a human? Most probably not.

Interesting.

Well, my only source was from a Cambridge graduate (working in the codebreaking faculty). I've not done much of my own research.

Initially difficult, but I was shown how to use it. Incredibly slow encrypting a message and it felt very 'bulky' - but it was definitely a worthwhile experience. If I remember correctly, the arrangement is not the usual "QWERTY" setup, since the German language has different frequency letters; arrangement is "QWERTZUIO" (1st row), "ASDFGHJK" (2nd row), and "PYXCVBNML" (3rd row). However, though the enigma machine was difficult to crack, and initially very successful for the Germans -- the British did eventually crack the code. They always ended their coded messages with "Heil Hitler", and, not only that, but they became rather careless with their alteration of the machine's three wheels; when you encrypt a code, you spin the wheels several times such that the order is completely different. Instead, the Germans decided to turn only the first wheel by 1 unit, meaning a pattern emerged in the enigma machine's code. They weren't particularly careful with the code configuration either; they published the new configurations monthly, which were accessible to the public -- which the British later discovered. It was the carelessness of the Germans that led to their codes being decrypted so quickly.

Good fun.

Hmm... I think I remember talking to a Cambridge under-grad about an uncrackable cipher, and replied that it was indeed possible to do so. Can't remember how, though.

Speaking of enigma machines - I feel honoured to have used one. It's amazing what luxuries history holds.

650 = 8[sup]3[/sup] + 2[sup]7[/sup] + 2[sup]3[/sup] + 4[sup]½[/sup]