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Topic: Archimedes number


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Pi

In the News (Tue 16 Jul 19)

  
  Archimedes - Wikipedia, the free encyclopedia
Archimedes became a popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the First and Second Punic Wars.
Archimedes was killed by a Roman soldier in the sack of Syracuse during the Second Punic War, despite orders from the Roman general, Marcellus, that he was not to be harmed.
Archimedes' On The Measurement Of The Circle Translated by Thomas Heath.
en.wikipedia.org /wiki/Archimedes   (2010 words)

  
 Archimedes of Syracuse the Mathematician (2 / 2)
Archimedes of Syracuse the Mathematician (2 / 2)
The 7th unit of 2 myriad 5819th numbers, and the 7602 myriad 7140th unit of 2 myriad 5815th numbers, and the 6486 myriad 8182nd unit of 2 myriad 5817th numbers,...,and the 9738 myriad 2340th unit of 3rd numbers, and the 6626 myriad 7194th unit of 2nd numbers, and 5508 myriad 1800.
Archimedes determines the centre of gravity of a parallelogram, a triangle, a trapezium, of a segment of a parabola.
www.mlahanas.de /Greeks/ArchimedesMath2.htm   (920 words)

  
 10.2. Archimedes (287? -212 B.C.)
Born in 287 B.C., in Syracuse, a Greek seaport colony in Sicily, Archimedes was the son of Phidias, an astronomer.
Archimedes proved to be a master at mathematics and spent most of his time contemplating new problems to solve, becoming at times so involved in his work that he forgot to eat.
When Archimedes was buried, they placed on his tombstone the figure of a sphere inscribed inside a cylinder and the 2:3 ratio of the volumes between them, the solution to the problem he considered his greatest achievement.
web01.shu.edu /projects/reals/history/archimed.html   (846 words)

  
 Stamps of Archimedes
The image of Archimedes represented on the stamp is from a bust in the National Museum of Naples, Italy.
The illustration of Archimedes is adapted from a Renaissance mosaic depicting his death.
In the background is a diagram of a laboratory apparatus commonly used to demonstrate Archimedes' Law of Buoyancy.
www.mcs.drexel.edu /~crorres/Archimedes/Stamps/stamps.html   (382 words)

  
 Archimedes
Archimedes was born in Syracuse, Sicily in 287 B.C. He was the son of Phidias, an astronomer.
Archimedes was not satisfied with the definition of pi as 3 1/7 0r 22/7.
Archimedes found that the gold had more mass than the crown, thus not all the gold was in the crown.
www.andrews.edu /~calkins/math/biograph/bioarch.htm   (1157 words)

  
 Archimedes - Early Years and Mathematics - Succeed through Studying Biographies
Archimedes showed that the surface of a sphere is four times that of a great circle, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder, and that the surface of a sphere is two-thirds the surface of a circumscribed cylinder including its bases.
He said that this number was large enough to count the number of grains of sand which could be fitted into the universe.
Archimedes was born in Syracuse, Sicily, but he was educated in Egypt by followers of the famous mathematician, Euclid.
www.school-for-champions.com /biographies/archimedes.htm   (1268 words)

  
 Pi - Open Encyclopedia   (Site not responding. Last check: 2007-10-18)
Pi is an irrational number: that is, it cannot be written as the ratio of two integers.
This result establishes the impossibility of squaring the circle: it is impossible to construct, using ruler and compass alone, a square whose area is equal to the area of a given circle.
The symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle.
open-encyclopedia.com /Pi   (2372 words)

  
 Read about Pi at WorldVillage Encyclopedia. Research Pi and learn about Pi here!   (Site not responding. Last check: 2007-10-18)
This means that it is impossible to express π using only a finite number of integers, fractions and their square roots.
the largest number of digits of π calculated on a home computer, 25,000,000,000, was calculated with pifast in 17 days.
the most pressing open question about π is whether it is a normal number -- whether any digit block occurs in the expansion of π just as often as one would statistically expect if the digits had been produced completely "randomly".
encyclopedia.worldvillage.com /s/b/Pi   (1995 words)

  
 Ancient Greek Number System
Diophantus extended the notion of number to include negatives and rationals, describes his symbols for exponents from -6 to 6, and notes that he moved beyond Greek traditions in permitting addition of non-homogeneous magnitudes.
The English names of the numbers 16 and 26 are sixteen and twenty six (and not six twenty) respectively, i.e there is a change of order.
Greek alphabetic numerals were favoured by the mathematician and physicist Archimedes, the scientific philosopher Aristotle and the mathematician Euclid, amongst others.
www.mlahanas.de /Greeks/Counting.htm   (1360 words)

  
 Archimedes' Approximation of Pi
Archimedes' Approximation of Pi Archimedes' Approximation of Pi One of the major contributions Archimedes made to mathematics was his method for approximating the value of pi.
Archimedes' method is new in that it is an iterative process, whereby one can get as accurate an approximation as desired by repeating the process, using the previous estimate of pi to obtain a new one.
Archimedes' method, as he did it originally, skips over a lot of computational steps, and is not fully explained, so authors of history of math books have often presented slight variations on his method to make it easier to follow.
itech.fgcu.edu /faculty/clindsey/mhf4404/archimedes/archimedes.html   (1092 words)

  
 Archimedes and the Computation of Pi
He invented the Screw of Archimedes, a device to lift water, and played a major role in the defense of Syracuse against a Roman Siege, inventing many war machines that were so effective that they long delayed the final sacking of the city.
Eratosthenes of Cyrene was a contemporary of Archimedes (Eratosthenes was about ten years younger), and the two corresponded on various matters.
The smallest possible number of sides is of course 3, corresponding to a triangle.
www.math.utah.edu /~alfeld/Archimedes/Archimedes.html   (910 words)

  
 December 2003
Archimedes began with a known fact – how many grains of sand would equal the diameters of a poppy seed – and began to extrapolate.
His final estimation of the number of grains of sand needed was 1 followed by 80 million billion zeros.
Numbers of this magnitude are commonplace in cryptography.
educ.queensu.ca /~fmc/december2003/LargeNumbers.html   (409 words)

  
 Dimensionless number   (Site not responding. Last check: 2007-10-18)
In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units; it does not change if one alters one's system of units of measurement, for example from English units to metric units.
Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all units cancel.
Dimensionless numbers are widely applied in the field of mechanical and chemical engineering.
www.worldhistory.com /wiki/D/Dimensionless-number.htm   (857 words)

  
 The Sand Reckoner   (Site not responding. Last check: 2007-10-18)
There are some, king Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited.
It follows that the last number in this scheme is the last number in the Qth order of the Qth period, or (in words) P to the 10th to the 8th.
The latter number consists of 6 units of the second order plus 40,000,000 units of the first order, a quantity that is not more than 10 units of the second order in Archimedes’ numbering scheme.
www.math.uwaterloo.ca /navigation/ideas/reckoner.shtml   (1496 words)

  
 Glimpses of Genius: Science News Online, May 15, 2004   (Site not responding. Last check: 2007-10-18)
Archimedes was not the puzzle's inventor—it was around before his time, says Reviel Netz, a Stanford University math historian on the team of experts studying the palimpsest.
The word suggested a novel possibility to Netz: Archimedes had been concerned not with the various shapes that can be made from the puzzle pieces but with how many different ways the pieces can be positioned to make a square.
Diaconis speculates that Archimedes might have been using the Stomachion to construct a pictorial proof of some geometric result such as the Pythagorean theorem, the famous equation relating the lengths of the two shorter sides of a right triangle and the length of the hypotenuse.
www.sciencenews.org /articles/20040515/bob9.asp   (2237 words)

  
 Archimedes Plutonium   (Site not responding. Last check: 2007-10-18)
And the numbers of the real line are a mirrow of the > operations + - * / and lim, but not of the operation sqrt.
I have intuited that the number of dimensions is limited to 3rd dimension because physics works for electrons having 3rd dimension and nothing higher than 3rd.
Numbers are intimately connected to operators and neither have an independent existence.
www.iw.net /~a_plutonium/File121.html   (3783 words)

  
 New Page 3
Pi is approximately 3.14 which is, "the number of times that a circle’s diameter will fit around the circle" (Witcombe, p.1).
Archimedes tried methods such as using large polygons to come up with number that would work.
The numbers 3.14 have been used to represent Pi for so long now by educators, that it is a very excepted number.
home.olemiss.edu /~mkyarbor/new_page_3.htm   (639 words)

  
 Archimedes
Stories about Archimedes are derived from the writings of Plutarch (born 250 years after the death of Archimedes).
Archimedes has to give the dimensions of the universe and uses a system with the sun at the center with planets (including earth) revolving round it.
For about 2000 years large numbers were ignored--the great mathematician Gauss said infinity should only be used as "a way of speaking" and not as a mathematical value.
mooni.fccj.org /~ethall/archmede/archmede.htm   (1010 words)

  
 Dimensionless number - InfoSearchPoint.com   (Site not responding. Last check: 2007-10-18)
A dimensionless number is a quantity which describes a certain physical system and which is a pure number without any physical units.
According to the Buckingham π-theorem of dimensional analysis, the functional dependence between a certain number (e.g.: n) of variables can be reduced by the number (e.g.
Reynolds number (This is the most important dimensionless number; it describes the fluid flow regime)
www.infosearchpoint.com /display/Dimensionless   (427 words)

  
 Articles - Pi   (Site not responding. Last check: 2007-10-18)
In Euclidean plane geometry, π may be defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius.
Because the coordinates of all points that can be constructed with ruler and compass are constructible numbers, it is impossible to square the circle, that is, it is impossible to construct, using ruler and compass alone, a square whose area is equal to the area of a given circle.
Nehemiah, a late antique Jewish rabbi and mathematician explained this apparent lack of precision in π, by considering the thickness of the basin, and assuming that the thirty cubits was the inner circumference, while the ten cubits was the diameter of the outside of the basin.
www.worldmapa.com /articles/Pi   (2720 words)

  
 No. 1823: Zero
When Archimedes wanted to show how large numbers might get, he began with a known Greek word, myriad.
Archimedes said, imagine a myriad grains of sand making up a pile the size of a seed.
Archimedes arrives at a number of grains of sand equal to a one followed by sixty-three zeros.
www.uh.edu /admin/engines/epi1823.htm   (592 words)

  
 Recursive Functions
Hence, if a is a number, a + b represents what is obtained by executing b times on a the operation +, that is the successor of a of order b, i.e., the sum of a and b.
and it is known that this is the least possible number of moves needed to solve the problem.
The procedure is similar to a classical method to compute approximations to real numbers which are solutions to algebraic equations, implicitly defining real numbers by circular definitions involving the number itself.
plato.stanford.edu /entries/recursive-functions   (6936 words)

  
 NTTI: Lesson Plans
Ask in a classroom discussion why Archimedes used straight lines (answer is because he could measure straight lines) and the greatest number of sides he used (answer is 96).
Ask students to write on their handout at least 3 different choices of the number of sides (be sure your numbers for inside and outside are identical).
Tell students to write this number on their handouts and use their calculators to calculate the circumference of the earth in miles.
www.krma.org /ntti/lessons/math/alltw_ch.html   (2316 words)

  
 Math Lair - Really Large Numbers
Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand.
But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe"
Examples are Mersenne primes, and odd perfect numbers (no odd perfect has been found yet, though).
www.stormloader.com /ajy/reallife.html   (397 words)

  
 m41
Mathematicians encounter frequently problems of having to replace one object (number, function, figure, etc.) by another object of the same kind, which is in a sense sufficiently near to, but simpler than the original object.
This number has the same striking property as Archimedes' number: The actual error is less than could be expected for the denominator 113.
If the number of the year ends with two zeroes, but the number of hundreds is not an integer multiple of 4, the year is treated as ordinary year.
kr.cs.ait.ac.th /~radok/math/mat4/m41.htm   (1899 words)

  
 Dictionary of Meaning www.mauspfeil.net
Because the coordinates of all points that can be constructed with ruler and compass are constructible numbers, it is impossible to squaring the circle square the circle, that is, it is impossible to construct, using ruler-and-compass construction ruler and compass alone, a square whose area is equal to the area of a given circle.
User:MrJones MrJones 00:52, 25 Oct 2003 (UTC) :::Numbers with a non-recurring decimal expansion are irrational number irrational.
The definition of a constructible real number is a number which lies in a field gotten by taken a finite sequence of quadratic extensions of the rationals, i.e.
www.mauspfeil.net /pi.html   (10253 words)

  
 Math History Daily Schedule   (Site not responding. Last check: 2007-10-18)
Question for Discussion Forum: Often a description of the work of Archimedes is accompanied with the suggestion that his On the Measurement of the Circle and The Quadrature of the Parabola anticipated the calculus of Newton and Leibniz.
Question for Discussion Forum: Most histories of mathematics suggest that the work of Archimedes was the "high-water mark" of ancient mathematics and that much of the work that came after Archimedes was often derivative and certainly not ground-breaking.
Discussion Forum: One of the sections headings in chapter 11 of Dunham is titled, "The Challenge of the Infinite." Reflect on our study of the history of mathematics and explain why, even in the late 19th century, the understanding of the infinite continued to be such a challenge for mathematicians.
people.hsc.edu /faculty-staff/leec/math212/histassignsp04.htm   (1515 words)

  
 OEDILF - Word Search
, that is acceleration of gravity times length to the power of 3 times density of fluid times density difference between gas (or solid) and fluid by viscosity squared is one of the many dimensionless numbers used in engineering applications to write physical (or other) laws with a smaller number of variables.
So Stokes’ law describing the terminal rising velocity (u) of small gas bubbles in a liquid (say a glass of champagne), or the settling velocity of small solid spheres can be written as Re = Ar/18.
Cussler wrote in his book on Diffusion-Mass transfer in fluid systems: “These numbers are often named, and they are major weapons that engineers use to confuse scientists.”
www.oedilf.com /db/Lim.php?Word=Ar   (284 words)

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