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18 May 2024
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N 08:18 | Arc Length of Curve in Polar Coordinates/Function of Angle 5 changes history +1,240 [Prime.mover (5×)] | |||
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07:47 (cur | prev) +1,262 Prime.mover talk contribs (Created page with "== Theorem == Let $C$ be a curve embedded in a polar plane. <onlyinclude> Let the radial coordinate $r$ of $C$ be defined as a function of the angular coordinate $\theta$: :$r = \map f \theta$ The '''arc length''' $s$ of $C$ between $\theta = \alpha$ and $\theta = \beta$ is defined as: :$\ds s := \in...") |
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08:14 | Arc Length of Curve in Polar Coordinates/Function of Radius 5 changes history +101 [Prime.mover (5×)] | |||
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07:38 | Move log Prime.mover talk contribs moved page Arc Length of Curve in Polar Coordinates to Arc Length of Curve in Polar Coordinates/Function of Radius |
N 07:38 | Arc Length of Curve in Polar Coordinates diffhist +1,077 Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $C$ be a curve embedded in a polar plane. Let the angular coordinate $\theta$ of $C$ be defined as a function of the radial coordinate $r$: :$\theta = \map f r$ The '''arc length''' $s$ of $C$ between $r = u$ and $r = v$ is defined as: :$\ds s := \int_u^v \sqrt {1 + r^...") |
17 May 2024
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N 10:47 | Lemniscate of Bernoulli from Tangents to Rectangular Hyperbola 2 changes history +1,133 [Prime.mover (2×)] | |||
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10:47 (cur | prev) +33 Prime.mover talk contribs | ||||
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10:32 (cur | prev) +1,100 Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $\KK$ be a rectangular hyperbola. Let $\LL$ be the locus of the foot of the perpendicular from the origin to the tangents to $\KK$. Then $\LL$ is the '''lemniscate of Bernoulli'''. </onlyinclude> == Proof == :File:Lemniscat...") |
16 May 2024
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22:02 | Generating Function for Legendre Polynomials 4 changes history +481 [Prime.mover (4×)] | |||
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N 16:31 | Bonnet's Recursion Formula diffhist +396 Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $\map {P_n} x$ denote the Legendre polynomial of order $n$. '''Bonnet's Recursion Formula''' states: :$\paren {n + 1} \map {P_{n + 1} } x = \paren {2 n + 1} x \map {P_n} x - n \map {P_{n - 1} } x$ </onlyinclude> == Proof == {{ProofWanted}} {{Namedfor|Pierre Ossian Bonnet|cat = Bonnet}} Category:Legendre Polynomials") |
15 May 2024
14:17 | Euler-Poincaré Characteristic on Homeomorphic Simplical Complexes diffhist −28 Prime.mover talk contribs |
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N 09:50 | Method of Least Squares (Approximation Theory)/Examples/Arbitrary Example 1 2 changes history +1,703 [Prime.mover (2×)] | |||
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09:50 (cur | prev) +1,703 Prime.mover talk contribs (Created page with "== Examples of Method of Least Squares == <onlyinclude> Let $B$ be a false balance. $2$ items are weighed on $B$: first individually and then together. The recorded weights are: :$17 \, \mathrm g$ and $25 \, \mathrm g$ for the separate items :$40 \, \mathrm g$ for the combined weight. The '''Definition:Method of Least Square...") |
14 May 2024
N 20:49 | Principle of Least Action diffhist +1,434 Prime.mover talk contribs (Created page with "== Physical Law == <onlyinclude> The '''Principle of Least Action''' is a physical law which states the following: Let $S$ be a dynamical system moving under conservative forces from point $A$ to point $B$. The motion of $S$ takes place in such a way that the action has a Def...") |
13 May 2024
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N 16:26 | Law of Species 4 changes history +1,861 [Prime.mover (4×)] | |||
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16:12 (cur | prev) +21 Prime.mover talk contribs | ||||
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16:12 (cur | prev) +1,353 Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $T$ be a right spherical triangle whose angles are $A$, $B$ and $C$ and whose respective sides opposite those angles are $a$, $b$ and $c$. Let $C$ be the right angle of $T$. Then: :$(1): $A$ and $a$ are of the same species, and $B$ and $B$ are of...") |