Subject:
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Re: Pyramids
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Newsgroups:
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lugnet.general
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Date:
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Fri, 29 Jan 1999 04:24:44 GMT
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Viewed:
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825 times
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For any of you interested, here's how I came up with the slopes formula:
Layer 1 and 2 have no 2x2 slopes, they start at layer 3.
Layer 3 has 4, layer 4 has 8, 5 has 12, etc. (add 4 to each layer).
This gives the series: sum(0,0,4,8,12, ... ,4(n-1),4n) for layers 1 through n.
Since we can ignore layers 1 and 2 we can rewrite this as:
sum(4,8,12, ... ,4(n-3),4(n-2))
Factoring out 4: 4*sum(1,2,3, ... ,n-3,n-2)
The series sum(1,2,3,4,...,n-1,n) equals (n(n+1))/2, and plugging in our
series where n=n-2 we get:
4(n-2((n-2)+1))/2 = 2((n-2)(n-1) = 2(n^2-3n+2) = 2n^2-6n+4
Rob (who likes recreational mathematics)
On Fri, 29 Jan 1999 02:24:53 GMT, "Janet Zorn" <lighthouse@bonzai.net> wrote:
> Great job!
>
> You knew all that algebra and geometry had to be good for something
> someday.
>
> Sure enough - for building toys.
>
> Rob Farver wrote in message <36b1be61.7834646@lugnet.com>...
>
> :Incidentally, while writing Tom on this subject today I came up with
> the
> :following formulas for figuring out how many slopes it takes to build
> :a pyramid (assuming all 2x2 slopes as Tom is using):
> :
> :For any pyramid of height 'n' where (n>2),
> :
> :1x2 tri-faced slope - 2
> :2x2 corner slope - 4n-4 or 4(n-1) <-- 2nx2n baseplate
> :2x2 slope - 2n^2-6n+4
> :Total pieces - 2n^2-2n+2
>
>
+-------------------------------------------+
| Rob Farver - rfarver@rcn.com |
| http://www.farver.com/lego/ |
| http://members.ebay.com/aboutme/rfarver |
+-------------------------------------------+
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Message is in Reply To:
 | | Re: Pyramids
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| Great job! You knew all that algebra and geometry had to be good for something someday. Sure enough - for building toys. Rob Farver wrote in message <36b1be61.7834646@lu...et.com>... :Incidentally, while writing Tom on this subject today I came up (...) (26 years ago, 29-Jan-99, to lugnet.general)
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