three cubic acres (Nils Lid Hjort)
Pietro Reynaud-Bersanino
pierrebi at tiscalinet.it
Fri Mar 3 17:22:11 CET 2000
In DCML digest, Vol 1 #100, you wrote:
Message: 3
Date: Thu, 2 Mar 2000 13:27:15 +0100
Message-Id: <200003021227.NAA30563 at dioscuri.uio.no>
From: Nils Lid Hjort <nils at math.uio.no>
>I find it wonderful that Barks chose "three cubic acres"
>to describe the amount of money in Scrooge's bin. Since
>`acre' is a two-dimensional measure, of area, it would
>follow that the Ducks live in (m^2)^3-space, that is, in
>some six-dimensional space.
I immediately remembered some letters on some old Uncle Scroge about this
topic.
I found them and i scannennered for DCML. I hope could interest!
Maybe some of the writers are members?
Has anybody got Mr Keellam's letter in U$ #252 ? Please send it to me ... I
am being waitig to read it since 1991!!
=========================================================
MAIL BIN: UNCLE SCROOGE #256
Dear Editor
Mr. Kellam's letter in Uncle Scrooge #252 calls to our attention an
important mystery conceming the size of Uncle Scrooge's money bin: More
remarkable still, however, is the fact that Mr. Kellam's letter solves a
second mystery that has been troubling me for several months, while,
contrarywise, the second mystery appears to solve the first. Let me explain.
You see, a few months ago, when I received an Uncle Scroge comic book in
the mail, I hapeened to notice there was something extra enclosed wìthin
the comic book: It was a brittle, yellowed envelope which appeared to be
very old. Thinking that someone at the publishing house had accidentally
dropped an advertisement in with my subscrlption, I was about to throw it
away whén I noticed the letters S. McD. scribbled in pencil in one corner.
Then, as you may imagine, my curiosity was greatly aroused. I hastened to
open the envelope. Inside was a single sheet of paper containing the sketch
ot a cube. On examining the sketch more closely, I noticed that the six
sides of the cube had been carefully shaded in with cross-hatches. Beneath
the sketch, the following inscription appeared:
43,560 / 6 = 7,260
I pondered over the sketch for many hours, but to no avail; I could not
fathom its meaning. So matters countinued until I read Mr. Kellam's letter
today. Then, suddenly, the meaning of the old sketch became perfectly clear:
Mr. Kellam assumes that a cubic acre means the volume of a standard cube,
each side of which is one acre in area. As he competently shows, this
assumption appears to be inconsistent with the commonly assumed shape of
the money bin. However, suppose that the entire surface of the standard
cube is intended to equal one acre. Then, since an acre equals 43,560
square feet, each of the six faces of the standard cube must have an area
ot only 7,260 square feet. This seems to be exacley wnat tne mysterious
sketch was saying! Going on from here, we find that each ot the twelve
edges of the standard cube must be approximately 85.2 feet long.
Consequenttly, a cubic acre turns out to be about 618,593 cubic feet. Since
Scraoge's wealth occupies three cubic acres, this means that he has about
1,855,779 cubic feet of cash. Assuming, then, that his money has reached
the 100 foot mark on the depth gauge, we find that the square base of his
money bin is roughly 136 feet in width and length. This corresponds
perfectly with the usual cubical picture of the money bin, for it allows
the bin to rise 36 feet above the money level, which is roughy the amount
of empty space that one usually sees in drawings of the bin's interior.
I hope this clarifies things. Of course Scrooge, with the vast mathematical
abilities he has gained from constantly counting his wealth, knew it all
along. Now, can anybody explain how Scrooge's notes happened to get mailed
to me?
(Brian K. Schmidl Chelmsford, MA)
=========================================================
MAIL BIN: UNCLE SCROOGE #257
Dear Editor
As a follow-up to Flash Kellam's investigation into the projected size of
Scrooge's money bin, I have taken things a step further in order to
estimate the minimum net worth of his fortune.
Mr. Kellam arrived at a figure of 27,274,140 cubic feet for the size of the
money bin. Let us assume that Scrooge collected silver and gold coins in
equal amounts; this would imply that approximately 13,637,070 cubic feet of
the bin is occupied by each of the precious metals.
Now, silver has a density of 10.5 grams per cubic centimeter; gold has a
density of 19.3 grams per cubic centimeter. Since precious metals are
usually measured in troy ounces, we multiply by 0.0321507 ounces per gram
and 28,316.846 cubic centimeters per cubic foot to give densities of
9559.267 ounces per cubic foot for silver and 17,570,843 ounces per cubic
foot for gold. Multiplying these densities times the volumes above gives us
130,360,390,000 ounces of silver and 239,614,810,000 ounces af gold, in the
money bin.
At the time of this letter, silver was selling for approximately $4.00 an
ounce; gold was worth $400.00 an ounce. Scrooge's silver is thus worth
$521,441,560,000, and his gold would amount to something like
$95,845,924,000,000.00. So we conclude that in today's market his coins
alone are valued at over 96 trillion dollars. At the bottom of the bin, of
course, crushed under the immense weight of the metal above, lie the
fabulous greenbacks which make up the remainder of his umpticatillion,
fantasticatillion fortune.
(Doug Ftmpley Boulder, CO)
=========================================================
MAIL BIN: UNCLE SCROOGE #261
Dear Editor
In Uncle Scrooge #256, you printed a letter about the size ot Scrooge's
money bin. It gave a size of 136 feet square, 100 feet deep arid 36 feet
empty at the top. l'm afraid the calculations are somewhat off. Scrooge is
supposed to have 3 cubic acres of cash, and while acre is a measure of area
and not cubage in the usual sense, it is used in measuring volume. In
irrigation, water is measured by the acre-foot. One acre of area a foot
deep, 43,560 cubic feet is one acre-foot. So, l'd consider a cubic acre as
the square root of 43,560 = 208.71 feet on aside by the same in depth, that
works out to 9,091,408 cubic feet per cubic acre. Then multiply by 3 and
you get 27,274,224 cubic feet. Extract the cube root of this and you get
just a scratch over 301 feet.
As Scrooge has only 99 feet on the money gauge the 27,274,224 divided by 99
would yield an area of 275,497 square feet. Assuming it's a square
building, it'd be just a scratch under 525 feet along each side.
No matter how you measure it, it's a big pile of piastres.
(J.W. Burns - Brockville, Ontario Canada)
Dear Editor
Strictly speaking, unless Uncle Scrooge's world has six spatial dimensions,
the term "cubic acres" is meaningless. An acre is a measure of area,
equivalent to 43,560 square feet. A cubic acre would therefore measure
approximately 82,653,950.010.000 square feet. Scroge's money shoul be
measured in terms of volume - something that can expressed in terms of
cubic feet.
If you interpret "cubic acre" to mean a cube whose faces each span an acre,
then a cubic acre would be equivalent to approximately 9,091,421.781 squre
feet (or approximately 208.71 feet per edge). If the interior of the bin
were 100 feet high , and the bin had a square footprint, the square's sides
would each be approximately 522.248 feet long. It the bin's interior had a
square footprint that was 100 feet long on each side, the bin would have to
be approximately 2,727,427 feet high. For Scrooge to swim in the bin, the
dimensions would have to be larger.
(Ricky Chew - San Jose, CA)
Dear Editor
In response to whether Scrooge has six or nine cubic acres of cash . We
know that he has a 3 cubic acre petty cash bin, another 3 acre main bib
underneath, and there is very likely another 3 acre area for his gold
bullion. Therefore we can assume that the bin is about 9 cubic acres.
As for the value of the bullion, it's pretry high! One brick is 7" x 3 5/8"
x 1 3/4", and contains approximately 400 troy ounces of gold. If gold is
worth about 400 dollars per troy ounce, each brick is worth about 160,000
dollars. If one of Scrooge's cubic acres is 618,593 cubdc feet, and a gold
brick is about .026 cubic feet, therefore there are about 72,214,917 bricks
in storage. The total value of Scrooge's gold bricks is about
$11,554,386,560,000.
(Corey Ziemniak - Montgomery, AL)
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