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2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
In the 1960s a new set of axioms for Euclidean geometry, suitable for American high school geometry courses, was introduced by the School Mathematics Study Group (SMSG), as a part of the New math curricula. This set of axioms follows the Birkhoff model of using the real numbers to gain quick entry into the geometric fundamentals.
Date/Time Thumbnail Dimensions User Comment; current: 14:42, 13 April 2010: 1,275 × 1,650, 103 pages (628 KB): Adrignola {{Information |Description={{en|1=Supplemental material for the High School Geometry Wikibook, providing teachers with additional activities, puzzles, and games to allow for additional problem solving opportunities.}} |Source=ht
Birkhoff's axiomatic system was utilized in the secondary-school textbook by Birkhoff and Beatley. [2] These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known as SMSG axioms. A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. [3]
The news was an advancement on a system that the AI research lab had unveiled in January, called AlphaGeometry, that could solve geometry problems from the IMO about as well as top high school ...
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