My Doubling the Cube Experience

The Math

Those of you who study math and geometry will understand what I mean when I say that two of my favorite non-problems in geometry are 'doubling the cube' and 'squaring the circle'. To New Age people, a double cube is two cubes side by side, or a rectangular box; this is not what is intended when we speak of doubling a cube. There we mean constructing a cube that has twice the volume of an original cube. The notion of squaring a circle indicates constucting a circle that has 1) the same area as a given square or 2) the same perimeter as a given square.

John Michell suggests that all ancient temples entailed 'squaring the circle' somehow, and Michael Schneider recommends that there is just no way to square the circle mechanically, that is with a square, compass and a straight edge. If you look in William Striling's book The Canon, which both these men quote from all the time, you will see it mentioned that the 'old way' of constructiong a circle that was equal to a square in area, was to make the diameter of the circle 8/10ths of the diagonal of the square.

In a square with sides of 1, the diagonal is the square root of 2; in a square with sides of 10, the diagonal is 10 times the square root of 2. 8/10ths of that is 8 times the square root of two. The radius of that circle would be four times the square root of 2. As the area of a circle is Pi times the radius squared, we know the area to be Pi times 32, or 100.5312. If we divide 100 by Pi we get 31.83, which is real close for whole numbers. Our diameter needs to Really Be 7.99 times the square root of 2, instead of 8, but I believe that we can agree that we 'can work with' 8, as a substitute for 7.99 in this case.

Multiplying the square root of 2 by 7.99 we get 11.299, so that we can say that for a 10x10 square, a circle with a diameter of 11.299 has the same area. The circle has a diameter that is 113% of the sides of the square. You multiply the sides by 1.13 to get the diameter of the circle.

In terms of the perimeter, we know that in a circle C= Pi x D, so if a 10x10 square has a perimeter of 40 then 40 divided by Pi yields 12.732, meaning that a circle with a diameter of 12.732 has a circumference equal to the perimter of the 10x10 square. To find the diameter of the circle with an equal circumfernece increase a side by 127.32%. Multiply the side by 1.273 to get the diameter of the circle.

Consider the Great Pyramid with sides of 755 feet, where 755 x 1.2732 = 961.266, which when divided by 2 yields 480.6, the height of the pyramid.

As I said, to some people, doubling the cube entails doubling one dimension of the three on the cube. You can do the same thing in two dimensions with squares; you can double the area of your space by doubling one dimension making a 1x1 space into a 1x2 or a 2x1 space. But what is called for is a cube (or square in 2D) that has twice the volume (or area). Instead of 1, we want to 2. In the case of the square the sides would each be equal to the square root of 2. To double a square, we increase it by 1.4142 in two dimensions. For the cube, we increase each diemnsion by the cube root of 2.

The following is a look at the process that I call 'hijacking' someone's posts in a message board or a forum. In this case I had made a posting in the GRAHAM HANCOCK MESSAGES BOARDS that was dealing with cosmological schemes and the book Hamlet's Mill, and someone challenges me to double the cube, and they point to a 'problem' relating to doubling a cubic altar.

Hamlet's Mill and Archaic Cosmological Schemes
was my post at http://www.grahamhancock.com/phorum/read.php?f=1&i=277159&t=277159

(see the 10th post down, not addressed to me the poster directly)

Author: magisterchessmutt
Date: 07-Dec-09 06:15
http://www.grahamhancock.com/phorum/read.php?f=1&i=277235&t=277159

Hi Geoffss,

I guess Big Bytes is too buried in his thoughts to ponder such riddles as how does the name "Apollwn"-1061, solve the ancient Delian dilemma of "Doubling the Cube" as mentioned here: http://en.wikipedia.org/wiki/Doubling_the_cube

History
The problem owes its name to a story concerning the citizens of Delos, who consulted the oracle at Delphi in order to learn how to defeat a plague sent by Apollo.[2][3] (According to some sources however it was the citizens of Athens who consulted the oracle at Delos.[4]) The oracle responded that they must double the size of the alter to Apollo, which was in the shape of a cube. The Delians consulted Plato who in turn gave the problem to Archytas, Eudoxus and Menaechmus who solved the problem using mechanical means; this earned a rebuke from Plato for not solving the problem using pure geometry.

This should be relatively easy for some here to figure out I think.

Cheers,

Stephen

  • We presume he means 'altar' of course. What a stupid damn way to introduce a post. He couldn't direct it to me and say, try this on for size, he addresses himself to not-the-poster, inside of my post. Geoffss sez:

    Author: geoffss
    Date: 07-Dec-09 08:41

    Might even try it myself ...
    Don't hold your breath!

    geoffss
    BOF

  • People are still laughing over that post, including me. Thanks for that. Keep reading and you will see what I mean.

    bigbytes sez:
    http://www.grahamhancock.com/phorum/read.php?f=1&i=277286&t=277159

    To double a cube OR a sphere, you increase the side Or the radius by a factor of 1.26, 0r 126%. With a square, we can begin with 2 cubed which = 8 , then 2 x 1.26 = 2.52, and 2.52 cubed = 16.003.

    Try this. The problem is to figure the sides of a cube twice the volume of another. We have cube 1 and cube 2. The sides of cube 1 are equal to the cube root of 1, while the sides of cube 2 are equal to the cube root of 2.

    Therefore, the ratio between one cube and a cube with twice the volume is 1: cube root 2; when the cube root(2) = 1.25992105

    bigbytes http://www.grahamhancock.com/phorum/read.php?f=1&i=277994&t=277159

  • A response:

    Author: geoffss
    Date: 20-Dec-09 19:24

    Apols. if I've missed someone else proposing this! My humble suggestion builds on posts by others here: I suggest the function v = s cubed for s (side) = 1, 2, 3, 4 , 5, 6, 7, 8, 8 10 .... n

    So, if v (volume) = 40, say, then 2v = 80 on the v axis and that will read off the s axis somewhere near 4.3?

    I suggest this as a more practical solution than the cube root approach - although I do like the simplicity of that as a theoretical idea. Don't see how you actually draw it, though.

    geoffss
    BOF

  • You will notice that in a cube, V equals the side cubed, so his graph that he is suggesting is graphing a side to the side cube, which is the same thing as a cube root chart. Read one way, you get cubes, read the other, you get cube root. However Geoff doesn't realize that and writes that his method is somehow a more practical solution than the cube root approach? What a dumb ass. And he proves it by saying that he can't draw any of this stuff.

    In addition to being a dumb ass, Geoff is a sniper, in that he likes to single out targets and go after them like a very small dog would. By that I mean that they don't know when to quit, or that you would just as soon kick them hard as ever have to listen to that noise again. He appears to not understand just how stupid he looks. Check out how he answers a post of mine.

    [Author: geoffss
    Date: 05-Dec-09 19:28

    Nice post - good to see you back ... if you behave!

    "Greenwich is located at 51.4 north latitude." No it's not: Greenwich is at about 51.477 (51.5).

    geoffss
    BOF]

  • If you didn't know him, you might get the idea that he might have something going on. See his response to my posting the URL of a webpage.

    Author: geoffss
    Date: 06-Dec-09 20:56

    So if it's self-publicity you want ...

    As you know, as you thrive, so do I - sign my guestbook and put up your links. Whilst my start site - awugabunnies - still exists, I've moved updated stuff to www.geoffss.plus.com, and www.geoffss.plus.com/guestbook.htm and www.awugabunnies.co.uk/2.html are how I get to "rule" on Google and Yahoo et al.

    geoffss
    BOF

    Do me a big favor and go to those pages and have a look. (awugabunnies and geoffssplus, priceless.) He is a very good speller and will help you with yours, now if he could help with arthritic hands THAT would be a big help. Consider that he has suggested that my signing the guest book at his site would drive traffic to mine. Notice where he suggests that he 'rules' something at Yahoo and Google. I told him that I would link to him but didn't want my URL in his book. FOR GOD'S SAKE, go to Geoffss' site and sign his guestbook. He is always good for at least a laugh. As I say, take a look at his stuff.

    1) http://www.geoffss.plus.com GEOFFSS PLUS

    2) http://www.geoffss.plus.com/movingmenhirs.htm MOVING MENHIRS (some transparent gifs should be converted)

    3) http://www.geoffss.plus.com/perpetualchoirs.htm THE PERPETUAL CHOIRS OF BRITAIN

    4) http://www.geoffss.plus.com/tarotII.htm Tarot II (do a search for 'bigbytes' on this page and see how many you find)

    5) http://www.geoffss.plus.com/jesusandjohn.htm JESUS AND JOHN

    6) http://www.geoffss.plus.com/stonehengestationstones.htm STONEHENGE - STATION STONES

    7) http://www.geoffss.plus.com/isis.htm ISIS

    8) http://www.geoffss.plus.com/ladyandgoat.htm LADY AND GOAT (that is the pentagram viewed two ways)

    9) http://www.geoffss.plus.com/mirrors!.htm MIRRORS!

    10) http://www.geoffss.plus.com/royalwatchers.htm THE FOUR ROYAL WATCHERS

    11) http://www.geoffss.plus.com/guestbook.htm GUESTBOOK

    Try going to each one of his pages and doing a search for the string 'bigbytes'. I saw seven on one page. On the Tart II page he addresses a probelm to me that he has never presented in a message. He writes,

    "Metatron's Cube - 8 of 10 points here coincide with the Tree of Life. Sephira 2 and 3 do not (but I recommend you visit the Bigbytes' sites given below for more here). 2 and 3 are 'found', I note (he doesn't!) by seed/vesica construction - 15, 75, 90 degree triangles."

    He may NOTE but he doesn't illustrate it in any way on that page. If you look at the image above, you see that all you have to do to find the top spheres in the tree, which are the top two points of the pentagram, is to entend the top sides of the (blue) hexagon. 'Seed/vesica construction' huh?

    "Let a man offer the least indignity to an Irish poet, even centuries after he had forfeited his priestly functions to the Christian cleric, and he would compose a satire on his assailant which would bring out black blotches on his face and turn his bowels to water." from The White Goddess by Robert Greaves, page 22.

    DC Symbols Homepage