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The oldest known multiplication tables were used by the Babylonians about 4000 years ago. [2] However, they used a base of 60. [2] The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. [2] "Table of Pythagoras" on Napier's bones [3]
It can be a printed page that a child completes with a writing instrument. No other materials are needed. In education, a worksheet may have questions for students and places to record answers. In accounting, a worksheet is, or was, a sheet of ruled paper with rows and columns on which an accountant could record information or perform calculations.
Because the cancellation property holds for groups (and indeed even quasigroups), no row or column of a Cayley table may contain the same element twice. Thus each row and column of the table is a permutation of all the elements in the group. This greatly restricts which Cayley tables could conceivably define a valid group operation.
The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. [1]
However, the questions may take different angles depending upon the ‘intelligence’ of the question setters. [3] [9] [7] Practice questions will include: If a piece of rope cost 20 cents per 2 feet, how many feet can you buy for 30 dollars? Which of the numbers in this group represents the smallest amount? (a) 0.3 (b) 0.08 (c) 1 (d) 0.33
The fraction 1 / 49 is a repeating decimal with a period of 42: 1 / 49 = 0. 0204081632 6530612244 8979591836 7346938775 51 (42 digits repeat) There are 42 positive integers less than 49 and coprime to 49.
Peter Steiner's 1993 cartoon, as published in The New Yorker "On the Internet, nobody knows you're a dog" is an adage and Internet meme about Internet anonymity which began as a caption to a cartoon drawn by Peter Steiner, published in the July 5, 1993 issue of the American magazine The New Yorker.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.