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In the 2nd century AD, the Greco-Egyptian astronomer Ptolemy (from Alexandria, Egypt) constructed detailed trigonometric tables (Ptolemy's table of chords) in Book 1, chapter 11 of his Almagest. [11] Ptolemy used chord length to define his trigonometric functions, a minor difference from the sine convention we use today. [ 12 ] (
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school (grades 9 to 12, for students typically aged 14 to 18), while seventeen states and the District of Columbia require four. [2]
[10] [11] Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. Von Neumann's work in game theory culminated in his 1944 book Theory of Games and Economic Behavior, co-authored with Oskar Morgenstern. [12]
A bijection with the sums to n is to replace 1 with 0 and 2 with 11. The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2 F n . For example, out of the 16 binary strings of length 4, there are 2 F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110.
This is an accepted version of this page This is the latest accepted revision, reviewed on 6 February 2025. Education in the United States of America National education budget (2023-24) Budget $222.1 billion (0.8% of GDP) Per student More than $11,000 (2005) General details Primary languages English System type Federal, state, local, private Literacy (2017 est.) Total 99% Male 99% Female 99% ...
The average student takes about 10 of these tests per year (e.g., one or two reading comprehension tests, one or two math tests, a writing test, a science test, etc.). [59] The average amount of testing takes about 2.3% of total class time (equal to about four school days per year).
This article needs to be updated. The reason given is: Many outdated sources and information (older than five years). Please help update this article to reflect recent events or newly available information. (July 2024) Medical condition Major depressive disorder Other names Clinical depression, major depression, unipolar depression, unipolar disorder, recurrent depression Sorrowing Old Man (At ...