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A description of the projective geometry can be constructed in the geometric algebra using basic operations. For example, given two distinct points in RP n−1 represented by vectors a and b the line containing them is given by a ∧ b (or b ∧ a). Two lines intersect in a point if A ∧ B = 0 for their bivectors A and B. This point is given ...
Condensed versions of the full Schaum's Outlines called "Easy Outlines" started to appear in the late 1990s, aimed primarily at high-school students, especially those taking AP courses. These typically feature the same explanatory material as their full-size counterparts, sometimes edited to omit advanced topics, but contain greatly reduced ...
The American high-school geometry curriculum was eventually codified in 1912 and developed a distinctive American style of geometric demonstration for such courses, known as "two-column" proofs. [49] This remains largely true today, with Geometry as a proof-based high-school math class.
Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and functions. Nearly all countries throughout the ...
Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension. Glossary of differential geometry and topology; Glossary of general topology; Glossary of Riemannian and metric geometry; Glossary of scheme theory; List of algebraic geometry topics
The left radical and right radical of the form B are the kernels of B 1 and B 2 respectively; [2] they are the vectors orthogonal to the whole space on the left and on the right. [3] If V is finite-dimensional then the rank of B 1 is equal to the rank of B 2. If this number is equal to dim(V) then B 1 and B 2 are linear isomorphisms from V to V ...
e 1, e 2, e 3 to the coordinate curves (left), dual basis, covector basis, or reciprocal basis e 1, e 2, e 3 to coordinate surfaces (right), in 3-d general curvilinear coordinates (q 1, q 2, q 3), a tuple of numbers to define a point in a position space. Note the basis and cobasis coincide only when the basis is orthonormal. [1] [specify]