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Show new changes starting from 15:11, 25 April 2024

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25 April 2024

11:57

Isometry Preserves Sequence Convergence‎ diffhist +16‎ Prime.mover talk contribs

			m 10:36		Riemannian Volume Form under Orientation-Preserving Isometry‎‎ 2 changes history +96‎ [Prime.mover‎ (2×)]
			m		10:36 (cur \| prev) +1‎ Prime.mover talk contribs
			m		10:36 (cur \| prev) +95‎ Prime.mover talk contribs

10:35

Smooth Mapping between Equidimensional Riemannian Manifolds is Local Isometry iff it is Isometry‎ diffhist +76‎ Prime.mover talk contribs

23 April 2024

07:38

Euler's Number is Transcendental‎ diffhist +404‎ Prime.mover talk contribs

m 06:20

Evolute of Ellipse/Cartesian Form‎ diffhist +13‎ Prime.mover talk contribs

22 April 2024

N 16:22

Inversive Transformation is Conformal Transformation‎ diffhist +1,139‎ Prime.mover talk contribs (Created page with "== Theorem == Let $\CC$ be a circle embedded in a Cartesian plane $\EE$ whose center $O$ is at the origin $\tuple {0, 0}$ and whose radius is $r$. Let $f$ be the '''inversive transformation''' of $\EE$ {{WRT}} $\CC$. Then $f$ is a Definition:Conformal Transformation|conformal transformatio...")

			N 15:52		Inverse of Curve under Inversive Transformation‎‎ 2 changes history +1,276‎ [Prime.mover‎ (2×)]
			m		15:52 (cur \| prev) +10‎ Prime.mover talk contribs
			N		15:52 (cur \| prev) +1,266‎ Prime.mover talk contribs (Created page with "== Theorem == Let $\CC$ be a circle embedded in a Cartesian plane $\EE$ whose center $O$ is at the origin $\tuple {0, 0}$ and whose radius is $r$. Let $f$ be the '''inversive transformation''' of $\EE$ {{WRT}} $\CC$. Let $P = \tuple {x, y}$ be an arbitrary point of $\CC$....")

21 April 2024

N 23:38

Inverse Function Theorem‎ diffhist +1,487‎ Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $n \in \N$ be a natural number. Let $f: \R^n \to \R^n$ be a mapping on the real Cartesian space of $n$ dimensions. Let $\mathbf x \in \R^n$ be an element of $\R^n$. Let the Jacobian matrix of $f$ be non-singular in the...")

			N 21:22		Inverse Element/Examples/Square Root Function‎‎ 3 changes history +1,433‎ [Prime.mover‎ (3×)]
					21:22 (cur \| prev) +28‎ Prime.mover talk contribs
			m		15:33 (cur \| prev) +1‎ Prime.mover talk contribs
			N		15:33 (cur \| prev) +1,404‎ Prime.mover talk contribs (Created page with "== Examples of Inverse Elements == <onlyinclude> Let $\struct {\CC, \circ}$ be the monoid of all real functions $\CC$ under composition $\circ$ over the closed real interval $\closedint 0 1$. Not all elements of $\CC$ have an inverse mapping, but in particular l...")

N 09:38

Invariant Measure of Image under Bijection‎ diffhist +892‎ Prime.mover talk contribs (Created page with "== Theorem == Let $\struct {X, \Sigma, \mu}$ be a measure space. Let $\theta: X \to X$ be an $\Sigma / \Sigma$-measurable bijection. Let $\mu$ be an invariant measure. Then: :$\forall A \subseteq X: \map \mu {\theta \sqbrk A} = \map \mu A$ == Proof == {{ProofWanted}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|...")

N 07:10

Algebraic Invariants for Group of Permutations of Variables‎ diffhist +1,261‎ Prime.mover talk contribs (Created page with "== Theorem == <onlyinclude> Let $S = \set {x_1, x_2, \ldots,x_n}$ be a set of algebraic variables. The algebraic invariants for the group of permutations of $S$ are those generated by the elementary symmetric polynomials: {{begin-eqn}} {...")

20 April 2024

23:39

Discriminant is Invariant for Isometry of Conic Section‎ diffhist +398‎ Prime.mover talk contribs

04:13

Projection from Product Category‎ diffhist +52‎ Leigh.Samphier talk contribs

19 April 2024

			23:02		Equation of Catenary/Cesàro‎‎ 2 changes history −235‎ [Prime.mover‎ (2×)]
					23:02 (cur \| prev) −227‎ Prime.mover talk contribs
					23:01 (cur \| prev) −8‎ Prime.mover talk contribs

			N 16:58		Equation of Catenary/Cesàro/Formulation 2‎‎ 3 changes history +1,267‎ [Prime.mover‎ (3×)]
			m		16:58 (cur \| prev) −53‎ Prime.mover talk contribs
					15:37 (cur \| prev) +90‎ Prime.mover talk contribs
			N		15:32 (cur \| prev) +1,230‎ Prime.mover talk contribs (Created page with "== Theorem == Consider a '''catenary'''. <onlyinclude> The '''catenary''' can be described by the Cesàro equation: :$a \rho = a^2 + s^2$ where: :$s$ is the arc length :$\rho$ is the radius of curvature :$a$ is a constant. </onlyinclude> == Proof == {{ProofWanted}} == Definition:Catenary/...")

			N 16:58		Equation of Catenary/Cesàro/Formulation 1‎‎ 7 changes history +782‎ [Prime.mover‎ (7×)]
					16:58 (cur \| prev) −53‎ Prime.mover talk contribs
					15:37 (cur \| prev) +90‎ Prime.mover talk contribs
					15:31 (cur \| prev) +74‎ Prime.mover talk contribs
					15:26 (cur \| prev) −90‎ Prime.mover talk contribs
					14:27 (cur \| prev) −4‎ Prime.mover talk contribs
					14:27 (cur \| prev) +21‎ Prime.mover talk contribs
			N		14:26 (cur \| prev) +744‎ Prime.mover talk contribs (Created page with "== Theorem == Consider a '''catenary'''. <onlyinclude> The '''catenary''' can be described by the Cesàro equation: :$a = \kappa {a^2 + s^2}$ where: :$s$ is the arc length :$\kappa$ is the curvature :$a$ is a constant. </onlyinclude> == Proof == {{:Equation of C...")

N 15:38

Equation of Catenary/Cesàro/Formulation 2/Proof‎ diffhist +370‎ Prime.mover talk contribs (Created page with "== Theorem == {{:Equation of Catenary/Cesàro/Formulation 2}} == Proof == <onlyinclude> {{ProofWanted}} </onlyinclude> == Historical Note == {{:Definition:Catenary/Historical Note}} == Lingustic Note == {{:Definition:Catenary/Linguistic Note}} Category:Cesàro Equation for Catenary")

			N 15:38		Equation of Catenary/Cesàro/Formulation 1/Proof‎‎ 2 changes history +370‎ [Prime.mover‎ (2×)]
					15:38 (cur \| prev) +27‎ Prime.mover talk contribs
			N		15:38 (cur \| prev) +343‎ Prime.mover talk contribs (Created page with "== Theorem == {{:Equation of Catenary/Cesàro/Formulation 1}} == Proof == {{ProofWanted}} == Historical Note == {{:Definition:Catenary/Historical Note}} == Lingustic Note == {{:Definition:Catenary/Linguistic Note}} Category:Cesàro Equation for Catenary")

			14:28		(Move log)‎ [Prime.mover‎ (2×)]
					14:28 Prime.mover talk contribs moved page Equation for Catenary/Cesàro to Equation of Catenary/Cesàro ‎
					14:21 Prime.mover talk contribs moved page Cesàro Equation for Catenary to Equation for Catenary/Cesàro ‎

N 14:21

Cesàro Equation for Catenary‎ diffhist +1,041‎ Prime.mover talk contribs (Created page with "== Curve == <onlyinclude> Consider a '''catenary'''. Let a cartesian plane be arranged so that the $y$-axis passes through the lowest point of the catenary. ==== Formulation 1 ==== {{:Equation of Catenary/Cesàro/Formulation 1}} ==== Formulation 2 ==== {{:Equation of Catenary...")

10:22

Euler's Number is Transcendental‎ diffhist +106‎ Prime.mover talk contribs

N 10:19

Euler's Number is Transcendental/Proof 3‎ diffhist +294‎ Prime.mover talk contribs (Created page with "== Theorem == {{:Euler's Number is Transcendental}} == Proof == <onlyinclude> {{ProofWanted}} {{qed}} </onlyinclude> == Historical Note == {{:Euler's Number is Transcendental/Historical Note}} Category:Euler's Number is Transcendental")

m 03:34

Integral to Infinity of Sine p x over x‎ diffhist 0‎ Robkahn131 talk contribs

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			N 21:22		Inverse Element/Examples/Square Root Function‎‎ 3 changes history +1,433‎ [Prime.mover‎ (3×)]
					21:22 (cur \| prev) +28‎ Prime.mover talk contribs
			m		15:33 (cur \| prev) +1‎ Prime.mover talk contribs
			N		15:33 (cur \| prev) +1,404‎ Prime.mover talk contribs (Created page with "== Examples of Inverse Elements == <onlyinclude> Let $\struct {\CC, \circ}$ be the monoid of all real functions $\CC$ under composition $\circ$ over the closed real interval $\closedint 0 1$. Not all elements of $\CC$ have an inverse mapping, but in particular l...")

			N 16:58		Equation of Catenary/Cesàro/Formulation 2‎‎ 3 changes history +1,267‎ [Prime.mover‎ (3×)]
			m		16:58 (cur \| prev) −53‎ Prime.mover talk contribs
					15:37 (cur \| prev) +90‎ Prime.mover talk contribs
			N		15:32 (cur \| prev) +1,230‎ Prime.mover talk contribs (Created page with "== Theorem == Consider a '''catenary'''. <onlyinclude> The '''catenary''' can be described by the Cesàro equation: :$a \rho = a^2 + s^2$ where: :$s$ is the arc length :$\rho$ is the radius of curvature :$a$ is a constant. </onlyinclude> == Proof == {{ProofWanted}} == Definition:Catenary/...")

			N 16:58		Equation of Catenary/Cesàro/Formulation 1‎‎ 7 changes history +782‎ [Prime.mover‎ (7×)]
					16:58 (cur \| prev) −53‎ Prime.mover talk contribs
					15:37 (cur \| prev) +90‎ Prime.mover talk contribs
					15:31 (cur \| prev) +74‎ Prime.mover talk contribs
					15:26 (cur \| prev) −90‎ Prime.mover talk contribs
					14:27 (cur \| prev) −4‎ Prime.mover talk contribs
					14:27 (cur \| prev) +21‎ Prime.mover talk contribs
			N		14:26 (cur \| prev) +744‎ Prime.mover talk contribs (Created page with "== Theorem == Consider a '''catenary'''. <onlyinclude> The '''catenary''' can be described by the Cesàro equation: :$a = \kappa {a^2 + s^2}$ where: :$s$ is the arc length :$\kappa$ is the curvature :$a$ is a constant. </onlyinclude> == Proof == {{:Equation of C...")