Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. Archimedes then estimated an upper bound for the number of grains of sand required to fill the Universe. A Greek stadium had a length of 600 Greek feet, and each foot was 16 dactyls long, so there were 9,600 dactyls in a stadium. Before you start counting, note this definition of a sand grain (as also mentioned above): http://answers.google.com/answers/threadview/id/539329.html, http://www.mnn.com/earth-matters/wilderness-resources/stories/are-there-more-grains-of-sand-on-earth-or-stars-in-the-sk, http://dictionary.reference.com/browse/sand, http://geo.msu.edu/extra/geogmich/sand.html.
To do this, he used the heliocentric model of Aristarchus of Samos. read more. Diameter of Earth around the Sun You could start off by trying to guess how many grains of sand there are in a spoon of sand. But I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the Earth filled up in the way described, but also that of the mass equal in magnitude to the universe. One experiment was to estimate the angular size of the Sun, as seen from the Earth. Subscribers get more award-winning coverage of advances in science & technology. But let’s continue marching bravely forward to see if we can tackle each of these sub-problems on their own, and then to see if this divide-and-conquer approach can help make the seemingly impossible possible.
Twenty grains make up about a centimeter, and 8,000 make up one cubic centimeter. I was taught that trying to count all the sand in the world is a project at worst frivolous and at best hopeless. They said, if you assume a grain of sand has an average size and you calculate how many grains are in a teaspoon and then multiply by all the beaches and deserts in the world, the Earth has roughly (and we're speaking very roughly here) 7.5 x 1018 grains of sand, or seven quintillion, five hundred quadrillion grains. The original work by Aristarchus has been lost. How many grains of sand are there on earth? In order to obtain an upper bound, Archimedes made the following assumptions of their dimensions: Archimedes then concluded that the diameter of the Universe was no more than 1014 stadia (in modern units, about 2 light years), and that it would require no more than 1063 grains of sand to fill it. If you took 10 sextillion grains of sand, put them into a ball, it would have a radius of 10.6 kilometers.
one grain of sand has a volume of 1.3 * 10^-9 cubic feet (from gomath.com) Some people on abc.net.au tried to figure out how many grains of sand are on earth. The Math Dude: Quick & Dirty Tips to Make Math Simpler. Are There More Men or Women in the World?
How many grains of sand in the Sahara [a reasonable & justified estimate expected]? Dr. Jason Marshall “The Math Dude” estimates the volume of the beaches to be 700 trillion cubic meters.
Since volume proceeds as the cube of a linear dimension ("For it has been proved that spheres have the triplicate ratio to one another of their diameters") then a sphere one dactyl in diameter would contain (using our current number system) 403, or 64,000 poppy seeds. Mathematically, the figure amounts to five sextillion grains of sand. In 2016 researchers, observing images from the Hubble Space Telescope stated that there could be more than 2 trillion galaxies in the observable universe, which is ten times more than the highest number expected. To make further calculations easier, he rounded up 640 million to one billion, noting only that the first number is smaller than the second, and that therefore the number of grains of sand calculated subsequently will exceed the actual number of grains. "Using this same principle, plus some additional information, mathematicians at the University of Hawaii tried to guess how many grains of sand are on the world's beaches.
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