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-   -   Double the area, Double the volume. (https://www.mersenneforum.org/showthread.php?t=6068)

 Uncwilly 2006-06-29 05:26

Double the area, Double the volume.

I was presented the following problem:
Using the classical tools (unmarked straight-edge, marking device, and a compass [not the direction pointer]), consider a square with sides of 1 unit and an area of 1 square unit. Please construct a square that has double the area, 2 square units.

I figured out how to do that, no problem.

Then I was presented with the follow on.
Given a cube with the dimensions of 1x1x1 unit, "construct" a cube of double the volume. Again you are limited to the classical tools, assume that they can work in 3D space or that you can work on a sheet of paper that will be folded up into the cube.

I haven't given that one a solid go. Please keep the math simple and spoilerise.

 Chris Card 2006-06-29 07:16

[spoiler]http://en.wikipedia.org/wiki/Duplicating_the_cube[/spoiler]

Chris

 mfgoode 2006-07-01 09:37

Doubling the cube.

[QUOTE=Chris Card][spoiler]http://en.wikipedia.org/wiki/Duplicating_the_cube[/spoiler]

Chris[/QUOTE]
:smile:
Uncwilly.
This problem has been one of the major 3 problems known since antiquity.

Its surprising that you should resurrect it here.

It was made aware to me by an excellent maths master (Christian Brother) who never restricted himself to the syllabus and I am thankful to him for giving me an all round view of maths even at that level.

Incidentally the same problem was known to the ancients and is mentioned in the Bible too but cloaked differently when the priests of Baal were asked to double the cubical altar that already existed IIRC.

Yes the Bible is not meant to be superficially read and to understand it esp. in these modern times we must pray to the Holy Spirit.

The Bible is eternally true and hence encompasses all modern theories and those to come but remember there is only ONE TRUTH. not only Science which is but a branch of a gigantic tree which coordinate in the trunk AND roots.

Mally :coffee:

 Uncwilly 2006-07-02 04:49

[QUOTE=mfgoode]This problem has been one of the major 3 problems known since antiquity.

Its surprising that you should resurrect it here.[/quote]
I had never run into this on before. I am not a math major and have had limited geometry experience.

I have found out (from following the links at the cited Wikipedia article), that for some odd reason, a politcal group has latched onto this:ernst: . On of the followers:alien: of the founder of the group is the one that posed to me the problem.

Again, after looking at the above cited article, it seems that it was not Baal's followers.
Can you point to me the place in Bible were it shows up????

[QUOTE=mfgoode]Yes the Bible is not meant to be superficially read and to understand it esp. [B]in these modern times we must pray to the Holy Spirit[/B].[/QUOTE]This is better suited to the Soapbox. If you do bring it up there, please give a reference to back your claim.

 mfgoode 2006-07-02 13:12

Doubling the cube.

[QUOTE=Uncwilly]I had never run into this on before. I am not a math major and have had limited geometry experience.

I have found out (from following the links at the cited Wikipedia article), that for some odd reason, a politcal group has latched onto this:ernst: . On of the followers:alien: of the founder of the group is the one that posed to me the problem.

Again, after looking at the above cited article, it seems that it was not Baal's followers.
Can you point to me the place in Bible were it shows up????

This is better suited to the Soapbox. If you do bring it up there, please give a reference to back your claim.[/QUOTE]

Uncwilly: No matter. Strange how knowledge is intertwined.
You are right its not exactly mentioned in the Bible but has a connection from Greek Mythology.
However Elijah did build an altar 1Kings 18:32 KJV. The whole chapter should be read to get the full reference to the Context and matter under discussion.

For the problem itself and the two other related problems and the clear account of the doubling of the altar read a bit down

[url]http://www.encyclopedia.jrank.org/[/url] CRE_DAH/CUBE_Gr_K46os

Mally :coffee:

 mfgoode 2006-07-02 13:26

Doubling the cube.

[QUOTE=Uncwilly]I had never run into this on before. I am not a math major and have had limited geometry experience.

I have found out (from following the links at the cited Wikipedia article), that for some odd reason, a politcal group has latched onto this:ernst: . On of the followers:alien: of the founder of the group is the one that posed to me the problem.

Again, after looking at the above cited article, it seems that it was not Baal's followers.
Can you point to me the place in Bible were it shows up????

This is better suited to the Soapbox. If you do bring it up there, please give a reference to back your claim.[/QUOTE]

Uncwilly: No matter. Strange how knowledge is intertwined.
You are right its not exactly mentioned in the Bible but has a connection from Greek Mythology.
However Elijah did build an altar 1Kings 18:32 KJV. The whole chapter should be read to get the full reference to the Context and matter under discussion.

For the problem itself and the two other related problems and the clear account of the doubling of the altar read a bit down

[url]http://www.encyclopedia.jrank.org/CRE_DAH/CUBE_Gr_K46os[/url]

Mally :coffee:

 brunoparga 2006-07-02 23:59

Bible and Pi

I can't quote book and verse and everything but there's some place in the Bible where it says that pi *equals* three.

 mfgoode 2006-07-03 11:04

Pi and Bible.

[QUOTE=brunoparga]I can't quote book and verse and everything but there's some place in the Bible where it says that pi *equals* three.[/QUOTE]
:smile:
An astute observation but not quite correct.

Refer Book 1 Kings ch.7 verse 23.[ KJV.]

Mally :coffee:

 mfgoode 2006-07-03 16:02

URL

[QUOTE=mfgoode]Uncwilly: No matter. Strange how knowledge is intertwined.
You are right its not exactly mentioned in the Bible but has a connection from Greek Mythology.
However Elijah did build an altar 1Kings 18:32 KJV. The whole chapter should be read to get the full reference to the Context and matter under discussion.

For the problem itself and the two other related problems and the clear account of the doubling of the altar read a bit down

[url]http://www.encyclopedia.jrank.org/CRE_DAH/CUBE_Gr_K46os[/url]

Mally :coffee:[/QUOTE]

:surprised
Uncwilly: I have had trouble opening up this URL given above from this forum.
Maybe you have too.
Well, Where there is a will there is a way.

Google - Chios doubling the cube- select about the third entry down
which is CUBE and you should get the works- all three problems I mentioned
and their solutions why they cannot be solved plus the account of the DELIAN priests and doubling the cubical altar.
So the origin is Greek Mythology and not Biblical.
All the best
Mally :coffee:

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