翻訳と辞書 Words near each other ・ The Sanatorium of the deported at Ikaria ・ The Sanctuary ・ The Sanctuary (Derby) ・ The Sanctuary (disambiguation) ・ The Sanctuary (recording studio) ・ The Sanctuary Lamp ・ The Sanctuary Sparrow ・ The Sand ・ The Sand and the Stars ・ The Sand Band ・ The Sand Castle ・ The Sand Child ・ The Sand Dwellers ・ The Sand Pebbles ・ The Sand Pebbles (film) ・ The Sand Reckoner ・ The Sand That Falls ・ The Sandals ・ The Sandbaggers ・ The Sandbox (play) ・ The Sandbox (video game) ・ The Sandcastle ・ The Sandcastle (disambiguation) ・ The Sandcastle (novel) ・ The Sanderson Centre ・ The Sandfleas ・ The Sandie Shaw Supplement ・ The Sandkings ・ The Sandkings (band) ・ The Sandlot Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク The Sand Reckoner ： ウィキペディア英語版 The Sand Reckoner ''The Sand Reckoner'' (, ''Psammites'') is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, he had to estimate the size of the universe according to the contemporary model, and invent a way to talk about extremely large numbers. The work, also known in Latin as ''Archimedis Syracusani Arenarius & Dimensio Circuli'', which is about 8 pages long in translation, is addressed to the Syracusan king Gelo II (son of Hiero II), and is probably the most accessible work of Archimedes; in some sense, it is the first research-expository paper.〔(Archimedes, The Sand Reckoner, by Ilan Vardi ), accessed 28-II-2007.〕 ==Naming large numbers== First, Archimedes had to invent a system of naming large numbers. The number system in use at that time could express numbers up to a myriad (μυριάς — 10,000), and by utilizing the word "myriad" itself, one can immediately extend this to naming all numbers up to a myriad myriads (108). Archimedes called the numbers up to 108 "first numbers" and called 108 itself the "unit of the second numbers". Multiples of this unit then became the second numbers, up to this unit taken a myriad-myriad times, 108·108=1016. This became the "unit of the third numbers", whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad-myriad times the unit of the 108-th numbers, i.e., $(10^8)^=10^$. After having done this, Archimedes called the numbers he had defined the "numbers of the first period", and called the last one, $(10^8)^$, the "unit of the second period". He then constructed the numbers of the second period by taking multiples of this unit in a way analogous to the way in which the numbers of the first period were constructed. Continuing in this manner, he eventually arrived at the numbers of the myriad-myriadth period. The largest number named by Archimedes was the last number in this period, which is ::$\backslash left((10^8)^\backslash right)^=10^$, necessary to manipulate powers of 10. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「The Sand Reckoner」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.