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From: "davide.mana@…" <davide.mana@…>

Date: Mon Mar 13, 2006 5:52 pm

Subject: The Castaigne collection - Two Other Items

ITEM #74512-T DICE SET

A slightly water-damaged wooden box of the kind used for carrying playing cards aboard of vessels (brass anchor set on the lid, brass finishing), now containing three blue granodiorite cubes (the side being roughly 5 cm) on the faces of which numbers were carved, probably for them to be used as playing dice, and obviously of great antiquity.

The first die carries the numbers 2, 3, 5, 7, 11, 13

The second die carries the numbers 1, 1, 2, 3, 5, 8

The third die carries the numbers 1, 3, 6, 10, 15, 21

The cubes are well-worn and slightly cracked. Isotope dating on the rock has proven inconclusive.

Woods-lamp analysis on the box revealed the remains of a blue-ink cargo stamp, based on which we can say for certain that the box was on board of the French warship Orient in 1798 and, on the inside of the lid, traces of Copper-bases blue blood (probably belonging to a horseshoe crab or similar crustacean).

Hope you gents like them.

Cheers

Davide Mana Torino, Italy

On 3/13/06, davide.mana@… <davide.mana@…> wrote: > > Trust the MiB to find a way to get me writing again… >

NYAH-HAHAHAHA! Dance for me puppet minion! Dance!

The first die carries the numbers 2, 3, 5, 7, 11, 13

The first six prime numbers…

The second die carries the numbers 1, 1, 2, 3, 5, 8

Fibonacci Sequence… Golden Spiral.

The third die carries the numbers 1, 3, 6, 10, 15, 21

The placement of the one's digit in the sequence 1 0 1 0 0 1 0 0 0 0 1 where the number of zeros increases in a geometric progression.

I imagine that the dice will mass a lot more than they should, being some kind of complicated hypercube where the sequences continue ad infinitum.

The Man in Black is : a friend of Google. Novus Ordo Seclorum : Annuit Coeptus : E Pluribus Unum

From: jonnyx@…

Date: Mon Mar 13, 2006 10:00 pm

On Mar 13, 2006 7:54 PM, The Man in Black <mib.zero@…> spaketh'd unto us thusly:

I imagine that the dice will mass a lot more than they should, being some kind of complicated hypercube where the sequences continue ad infinitum.

…and of course the numbers on each face will sometimes change after a roll…

A 4d hypercube will have 24 faces and 8x the mass of a normal 3d cube.

A 5d hypercube will have 80 faces and 40x the mass of a normal 3d cube.

Here's a chart with the progression:

http://gregegan.customer.netspace.net.au/APPLETS/29/HypercubeNotes.html

I could have saved myself an hour of calculations if I had simply checked online first instead of doing the math; 4d easy, 5d not so easy, 6d make brain hurt. I leave the numeric progression of each die as an exercise for the reader.

—jX

From: "ptender" <ptender@…>

Date: Wed Mar 15, 2006 3:10 pm

The third die carries the numbers 1, 3, 6, 10, 15, 21 » » The placement of the one's digit in the sequence 1 0 1 0 0 1 0 0 0 0 1 » where the number of zeros increases in a geometric progression.

Aha! now MIB is busted. By mere luck I noticed that his sequence for the third die would render 1, 3, 6, 11, 20, 37, 70: Fermat numbers! Not the triangular numbers inscribed in the third die of ITEM #74512-T.

Mana, check the wooden box. If there is evidence of a missing fourth die, I know where you may find it.

I was thinking simply: » 1 * » 2+1 = 3 » 3+3 = 6 » 4+6 = 10 » 5+10 = 15 » 6+15 = 21 > Maybe I'm a bit hard of thinking at the moment, but I don't get the progression

One can imagine points necessary to draw triangles. Just like a set of bowling pins or a rack of billiard balls. First row you have one, the second two, third three, fourth four… The ten bowling pins form a triangle with four rows. If you check the fourth number in Peter's table, it's 10. The fifteen billiard balls make a five row triangle - the fifth number is 15.

Thinking simply, Peter added the next number (left column) to the previous result (right). I've placed a 1 in his table (above) for clarification. Similar process is used to compose what we know as Pascal's Triangle. Something that, although described five hundred years earlier by Chinese mathematician Yanghui and the Persian astronomer-poet Omar Khayyám, is credited to Pascal.

Another way to get the nth triangular number is to multiply n by one more than n and then divide by 2.

But let me stop using bandwidth with OT stuff…

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