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In complex analysis, a Schwarz–Christoffel mapping is a conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon.Such a map is guaranteed to exist by the Riemann mapping theorem (stated by Bernhard Riemann in 1851); the Schwarz–Christoffel formula provides an explicit construction.
The heavily computational AP Physics B course served as the College Board's algebra-based offering for four decades. As part of the College Board's redesign of science courses, AP Physics B was discontinued; therefore, AP Physics 1 and 2 were created with guidance from the National Research Council and the National Science Foundation. [2]
Articles related to constructible regular polygons, i.e. those amenable to compass and straightedge construction. Carl Friedrich Gauss proved that a regular polygon is constructible if its number of sides has no odd prime factors that are not Fermat primes, and no odd prime factors that are raised to a power of 2 or higher.
Meanwhile, AP Physics 2 covered the other content areas. In 2020, the sound, waves, and electricity topics were removed from AP Physics 1 and moved to AP Physics 2. In 2024, the unit covering fluids was moved from AP Physics 2 to AP Physics 1, making space in the AP Physics 2 curriculum for more detail on waves and modern physics. [2] [7]
A skew zig-zag hexadecagon has vertices alternating between two parallel planes. A regular skew hexadecagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew hexadecagon and can be seen in the vertices and side edges of an octagonal antiprism with the same D 8d, [2 +,16] symmetry, order 32.
The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2] It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the ...
Riemann mapping theorem. If G ≠ C {\displaystyle G\neq \mathbb {C} } is a simply connected domain and a ∈ G {\displaystyle a\in G} , there is a unique conformal mapping f {\displaystyle f} of G {\displaystyle G} onto the unit disk D {\displaystyle D} normalized such that f ( a ) = 0 {\displaystyle f(a)=0} and f ′ ( a ) > 0 {\displaystyle ...
The unit covering electric circuits was changed to be more comprehensive, and Blackbody radiation and Compton scattering were added to Modern Physics as well. As of the fall of 2024, all AP Physics 2 units are numbered sequentially to those in AP Physics 1, starting with Thermodynamics as unit 9 and ending with Modern Physics as unit 15.