h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

This is by me... I was feeling bored in Maths and started working out how to calculate the volumes and surface areas of some solids... some of it's a bit obvious, but I think it would be quite useful...

Ooops... forgot to put the link

http://www.h2g2.com/A435755

there you go

Although I guessed that p was Pi, I couldn't find this mentioned anywhere. You just use p without saying what it is.

The length of a prism is not as obvious as it sounds. Consider placing a coin on the table. Put another coin one metre to the right of it on the table. Now lift the second coin up one centimetre without turning it. Join the two coins together by a surface. You have a prism. The length of the prism is one centimetre.

When you say that a sphere is the shape of a football, you are assuming a particular type of football. My rugby teacher used to say that "soccer is a game played with a grossly mis-shapen ball".

Well done for working out the volume of a torus. This took me about 3 pages of integration to check. I wasn't sure at first exactly what you meant by the "radius of the torus", but I worked it out in the end. A diagram would certainly make things easier.

Yes... I'll fix them, and add you to my "thanks to" section

p is a relic from my conversion to html codings... on my computer it appears as a pi symbol, but I'll add an explanation at the beginning.

Yes, rugby is the only type of football worth playing...

Thanks again...

I've now updated the entry...

I've now updated the entry...

Here's some hints & comments:

* Expand on the introduction a tad -- maybe something on where all these formulas came from.

* I agree that graphics would massively help, but that isn't something you need to worry about -- the h2g2 staff can theoretically take care of that.

* Maybe add something about when (outside of school exams) these formulas might be useful.

* I want to know how to calculate the surface area of a Klein bottle!


mikey

Okaaaay... klein bottle? Isn't that topography...?

Excellent!!!

You have just reminded me of some of the wonderful formulae that my maths master drummed into my head some thirty-odd years ao, that were instantly forgotten when I left school!!

Well done!!

'G'

*flattered*

Oh, thank you...

That's OK!!!!


'G'

π is the guideml for the pi symbol. The semicolon matters.
Or use .

We have an entry on pi - link to it. A211500
There's also an entry on the pyramids you might want - A577

You need to remove refs to 'I' and suchlike.

Examples of shapes for all shapes: eg for cuboid: "A cuboid is a shape all the sides of which are squares or rectangles, like a matchbox." You have some - but it'd be nice to have some for all.
Where appropriate, have examples that we have guide entries on, so you can odd pointless extra links...

Technically, I believe shapes have to be 2D - 3D things are called 'solids'. Hmm - anyone?

H2G2 should , not the 2s - it's a squared symbol, not a subscript. But that sentence needs to go anyway in the final thing. Try italicising such things and prefixing by 'notes to the sub-ed' - everyone reading will still know, but you'll avoid irritating people like me pulling you up on it.

The sphere is strange? I thought it was the simplest we got...

Probably worth mentioning the calculations for cubes as well - they're simpler than general cuboids...

One thing that was brought home to me as a result of feedback to my entry on entropy is that people *HATE* equations. Get rid of them - all of them. Where necessary, give a little more explanation in words - but generally you've done this already.
Seriously - equations will scare away everyone who didn't already know the answers...

Ok. This is where you start to hate me. If you want to expand your entry so people don't complain that "that this is the sort of thing that everybody should know anyway", then you need to say how you calculate the surface area and volume of arbitrary solids, which will shut up everyone short of A-level maths...

That's integration and suchlike - I have no idea how feasable it is to explain that lot sensibly, but who knows... *shrug*

You could also mention calculating volumes and surface areas of composite solids - so if you stick a triangular prism on top of a cuboid (like a house, say) the volume is equal to the sum of the volume of each subsolid. The surface area is added, less twice the surface area of where they touch. Similarly for solids shich are hollow - sphere with an empty square-shaped hole - subtract volume, and add surface area.

You could also talk about how volumes change when you stretch or twist solids. EG - if you double the size of a solid, surface area quadruples, and volume is multiplied by a factor of eight. Twisting increases surface area (not sure how, exactly), but leaves volume constant. Doubling size in only one direction (stretch) doubles volume, and will increase, but less than double, surface area.

As a practical application - the fact that volume increases by x8 and surface area increases by x4 is the reason why if you build a scale model of an aeroplane that flies, then scale it up to full size, the fullsize version probably won't fly very well - surface area (of the wings) provides lift, but volume provides weight, so there is less lift than weight, and it crashes into the hillside.

Other common solids - ellipsoids, I guess. They're complicated, but no worse than tori. {ellipsoids are sorta like rugby balls - they're what you get when you stretch or squash a sphere}.

You could talk about fractal objects like sierpinski's cube. They tend to have infinite surface area, and zero volume. Which is highly cool if you like that sorta thing...

Keep up the good work

btw - the list of things like π is at http://www.h2g2.com/A266951

Looks like I'll have to do quite a bit of work on it! within the next week, anyway... Thanks for the links!

The sphere is strange because of its simplicity... but I didn't make that clear.

You're right - 3D objects are called solids. I should have spotted that blatant mistake - I'm a 3D artist and all my apps call them solids. D'oh.

I don't understand your comments about . I've used that tag exclusively throughout my article - should I not have done that? What do you think about my formatting of the equations?

I'll add the cube equations as requested. I don't understand what you mean about getting rid of the equations. Without the equations there wouldn't be any point in the article. The times I've used more than one equations, the first is to show the fully expanded version so that the reader can see how it works... I'll also implement the explanation of how to break down complex solids into simple ones, and the principle of breaking surfaces into polygons.

I think I'll leave integration until I've done A-level. Working out the equations for the torus was hard enough *shudders*. Your other suggestions, i.e. the twisting/stretching/fractals are great but I feel that they would be best suited to being put into another article.

Thanks for the (constructive) criticism!

I've just been thinking - would it be better to do this as a UoL project?

One thing I found very confusing was the equation for the volume of a sphere. Without brackets, its unclear if you mean (4)/(3pr^3) (which is wrong), or the correct (4/3)*pr^3). I'm not sure of the best way round this - the brackets always feel cumbersome to me.

Recently I prepared an entry with some equations, besides that I am quite experienced as far as typography and formulas is concerned (LaTeX ). Here are my tips:

1. Numbers not in italics.
2. Use   rather than mere spaces within formulars unless you want to allow a line break there.
3. Unfortunately I can't reconstruct how you included special characters into your article. The correct form -- Lucinda mentioned that already -- is π or . Please use that also for your times symbols. Don't write p instead of pi.
4. Use instead of "-" for the minus sign.
5. Use for surface and volume S and V.
6. Put a   between number and unit. Even if the guidelines say something different. It's ugly and wrong.

Your article of course has the problem that its size is limited but there are myriads of polyhedra. So you must say something about calculating volumes, surfaces etc in general (popular scientific).
By the way, you may have a look at Guldin's rules.

Just put a   between 3 and pi.

When I say get rid of the equations, I mean get rid of the lettered versions - like "V=d³". Naturally you need to keep the expanded version - as you say, that's the entire point.

The thing I was talking about where you write H2G2 - you should write H²G².

You're assuming that h2g2 is a mathematical formula, in which case the 2's are superscript. If it is a chemical formula, like H2O, then they should be subscript. Why not leave them as normal script, like they appear under the logo at the top of this page?