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Whilst trying to work out areas of circles for my DIY Vulcan bomber project (See link (or not( suit yourself)))...I got bored of this pi times the wotsit squared.
Having a ponder....I thought a circle with a diameter of 1 [insert units of length of your choice] would have a certain area, now, if
we were to draw a square which has the same length sides it'll have an area of 1 [units] Obviously the circle is a bit smaller. In fact the circle will be roughly 0.785398175 of the area of the square
So, instead of all this faffing about with radius's and pi, we can just measure the diameter, multiply it 0.785398175 and you'll get a close-ish answer.
<exits to drum roll, and the odd tomato>
DIY Vulcan bomber.................................
Your_20own_20Vulcan_20bomber
[not_morrison_rm, Aug 06 2011]
aspirational pyramid
http://www.google.c...ved=1t:429,r:7,s:61
[not_morrison_rm, Aug 08 2011]
Tau
http://tauday.com/
If you don't like pi, try tau. Though it actually makes calculating the area of a circle slightly harder. [scad mientist, Aug 08 2011]
[link]
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0.785398175 is equal to 4/pi. |
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Same formula, just expressed differently. |
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<cocks ear to listen for arrival of fleet of trucks bringing rotten watermelons> |
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//Same formula, just expressed differently// |
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Yep.but much easier...honest guv. It's pi r 2 or dia x 0.785398175 ...which one looks easier to you? |
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Still wondering why they bothered teaching me it in school, possibly as example of using square roots? |
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...trucks bringing rotten watermelons..would those be the square ones grown in boxes, or the one with square roots...ha hahaha hahaha..ahem. |
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//Bad math. R^2 x 3.14, or D^2 x 0.785, will get you the area of a circle. D x 0.785 (the formula posted) will not.// |
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Not squaring the measurement _does_ make the equation simpler, and the _only_ cost is that it now only works for diameters of 1 unit. |
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//Pi times the wotsit squared// [marked-for-tagline] |
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//wotsit// One of the lesser-known characters in the
Greek alphabet. |
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I'll have you know my grandmother was a wotsit. |
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That sounds a bit cheesy ... |
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erm, did just try it on circles of radius of 1, 2, 2.5 and 3, so it does hold for most circles. |
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Actually, I got bored two weeks ago ran the idea past one of my students who's a post-grad in maths and he wrote up the proof of it. |
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To me, finding the diameter, squaring it and multiplying by 0.785 is a lot easier. It's mighty easy to me to work out squares but more tricky to work out (on paper) what the square root of anything is, as it seems to involve kind of ranging shots and then adjusting the figure being used. |
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That's my story and I'm sticking to it... |
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I rue the loss of the slide rule. |
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//I rue the loss of the slide rule.// |
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Can't get the parts for my steam abacus these days... |
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There's also the fact that pi shows up in all sorts of formulae completely unrelated to circles. It's a universal constant, not just for round things, and is therefore much more useful to learn. |
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In questions of taste there is no argument, so to me it is easier dia x dia then x 0.78 whatever, but to others it's not. |
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Anyway, next is how to work out the volume of [cute person of your choice] using only warm custard... |
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There is some considerable history of attampting to simplify Pi and it's equations. |
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The state of Indiana came very close to legally defining Pi as 4 in 1897. |
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I've also heard that one of the Pharaohs approximated to 2. His Pyramid no longer stands. |
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always fancied a pyramid meself, like the one in the workmen's village - the boss can have one, then so can I...see link |
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