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- 21:40, 8 March 2021 Condition for Straight Lines in Plane to be Parallel/Slope Form (hist | edit) [1,675 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $L_1$ and $L_2$ be straight lines in the Cartesian plane. Let the Definition:Slo...")
- 21:26, 8 March 2021 Angle between Straight Lines in Plane/General Form (hist | edit) [1,982 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $L_1$ and $L_2$ be straight lines embedded in a cartesian plane, given in Equation of Straight...")
- 19:08, 8 March 2021 Differentiation of Exponential of a x by Cosine of b x and Exponential of a x by Sine of b x wrt x as Invertible Matrix (hist | edit) [2,440 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $a, b, x \in \R$ be real numbers. Suppose $a \ne 0 \ne b$. Denote $\ds f_1 = \map \exp {a x} \map \cos {b x}$, $f_2 = \map \exp...")
- 08:22, 8 March 2021 Equation of Straight Line in Plane/Normal Form/Polar Form (hist | edit) [2,080 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\LL$ be a straight line such that: :the perpendicular distance from $\LL$ to the Defin...")
- 07:20, 8 March 2021 Equation of Straight Line in Plane/Two-Point Form/Determinant Form (hist | edit) [1,347 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\LL$ be a straight line embedded in a cartesian plane, given in Equation of Stra...")
- 06:56, 8 March 2021 Equation of Straight Line in Plane/Two-Point Form/Parametric Form (hist | edit) [1,665 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\LL$ be a straight line embedded in a cartesian plane, given in Equation of Stra...")
- 15:49, 7 March 2021 Riemann Zeta Function at Non-Positive Integers/Examples (hist | edit) [590 bytes] Robkahn131 (talk | contribs) (Created page with "== Examples of Use of Riemann Zeta Function at Non-Positive Integers == <onlyinclude> === Riemann Zeta Function at Non-Positive Integers/Examples/Zeta(-1)|Example: $\dis...")
- 15:49, 7 March 2021 Riemann Zeta Function at Non-Positive Integers/Examples/Zeta(-1) (hist | edit) [806 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Riemann Zeta Function at Non-Positive Integers == <onlyinclude> :$\map \zeta {-1 } = -\dfrac 1 {12} $ </onlyinclude> == Proof == Follows directly fr...")
- 15:49, 7 March 2021 Riemann Zeta Function at Non-Positive Integers/Examples/Zeta(-3) (hist | edit) [810 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Riemann Zeta Function at Non-Positive Integers == <onlyinclude> :$\map \zeta {-3 } = \dfrac 1 {120} $ </onlyinclude> == Proof == Follows directly fr...")
- 15:35, 7 March 2021 Position of Centroid of Triangle on Median (hist | edit) [1,995 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\triangle ABC$ be a triangle. Let $AL$, $BM$ and $CN$ be the medians of $\triangle AB...")
- 14:18, 7 March 2021 Span of Exponential of a x by Cosine of b x and Exponential of a x by Sine of b x is preserved under Differentiation wrt x (hist | edit) [1,898 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $a, b, x, \alpha_1, \alpha_2 \in \R$ be real numbers. Denote $\ds f_1 = \map \exp {a x} \map \cos {b x}$, $f_2 = \map \exp {a x}...")
- 09:28, 6 March 2021 Value of Position-Ratio (hist | edit) [898 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $P$ and $Q$ be points. Let $R$ be a point on the straight line passing through $P$ a...")
- 09:18, 6 March 2021 Position-Ratio of Point/Examples/R Midway between P and Q (hist | edit) [944 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Position-Ratio of Point == Let $P$ and $Q$ be points. Let $R$ be a point on th...")
- 09:16, 6 March 2021 Position-Ratio of Point/Examples/R Approaching Infinity (hist | edit) [1,032 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Position-Ratio of Point == Let $P$ and $Q$ be points. Let $R$ be a point on th...")
- 09:14, 6 March 2021 Position-Ratio of Point/Examples/R Approaching Q (hist | edit) [955 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Position-Ratio of Point == Let $P$ and $Q$ be points. Let $R$ be a point on th...")
- 09:12, 6 March 2021 Position-Ratio of Point/Examples/R Approaching P (hist | edit) [783 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Position-Ratio of Point == Let $P$ and $Q$ be points. Let $R$ be a point on th...")
- 19:26, 5 March 2021 Joachimsthal's Section-Formulae/Historical Note (hist | edit) [467 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Joachimsthal's Section-Formulae == <onlyinclude> This result is attributed to {{AuthorRef|Ferdinand Joachimsthal}} by {{AuthorRef|D.M.Y. Sommerville}...")
- 19:23, 5 March 2021 Joachimsthal's Section-Formulae (hist | edit) [1,659 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $P = \tuple {x_1, y_1}$ and $Q = \tuple {x_2, y_2}$ be points in the Cartesian plane. Let $R = \tuple {...")
- 17:10, 5 March 2021 Condition for 3 Points in Plane to be Collinear (hist | edit) [1,510 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $A = \tuple {x_1, y_1}, B = \tuple {x_2, y_2}, C = \tuple {x_3, y_3}$ be points in the Definition:Cartesian Plane|Cartes...")
- 16:51, 5 March 2021 Area of Triangle in Determinant Form/Proof 2 (hist | edit) [1,841 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Area of Triangle in Determinant Form}} == Proof == <onlyinclude> :400px Let $A$, $B$ and $C$ be as defined.. Let...")
- 16:02, 5 March 2021 Area of Triangle in Determinant Form/Proof 1 (hist | edit) [1,813 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Area of Triangle in Determinant Form}} == Proof == <onlyinclude> :400px Let $A$, $B$ and $C$ be defined as Definition:C...")
- 15:52, 5 March 2021 Reversal of Order of Vertices of Triangle causes Reversal of Sign of Area (hist | edit) [1,185 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\triangle ABC$ be a triangle embedded in the plane. Let $\Area \triangle ABC = \AA$. Then: :...")
- 14:37, 5 March 2021 Difference of Squares of Sines (hist | edit) [983 bytes] Robkahn131 (talk | contribs) (Created page with "== Theorem == <onlyinclude> {{begin-eqn}} {{eqn | l = \sin^2 A - \sin^2 B | r = \map \sin {A + B} \map \sin {A - B} }} {{eqn | l = \paren{\sin A + \sin B } \paren{\...")
- 01:36, 5 March 2021 Cardano's Formula/Examples (hist | edit) [230 bytes] Robkahn131 (talk | contribs) (Created page with "== Examples of Use of Cardano's Formula == <onlyinclude> === Example: $\displaystyle x^3 - 15x - 4$ === {{:Cardano's Formula/...")
- 01:33, 5 March 2021 Cardano's Formula/Examples/x^3 - 15x - 4 (hist | edit) [8,567 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Cardano's Formula == <onlyinclude> :$\ds x^3 - 15x - 4 = 0$ :has solutions $\tuple {4, \paren {-2 + \sqrt {3 } }, \paren {-2 - \sqrt {3 } } }$ </onl...")
- 21:42, 4 March 2021 Exponential of a x by Cosine of b x and Exponential of a x by Sine of b x are Linearly Independent (hist | edit) [1,004 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $t, a, b \in \R$. Then $e^{a t} \map \cos {b t}$ and $e^{b t} \map \sin {b t}$ are linearly independent...")
- 21:07, 4 March 2021 Linear Mappings between Vector Spaces form Vector Space (hist | edit) [5,676 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $\struct {F, +, \times}$ be a field whose unity is $1_F$. Let $X, Y$ be Definition:...")
- 17:47, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 1/Examples (hist | edit) [745 bytes] Robkahn131 (talk | contribs) (Created page with "== Examples of Use of Sum of Reciprocals of Powers as Euler Product/Corollary 1 == <onlyinclude> === Sum of Reciprocals of Powers as Euler Product/Corollary 1/Examples/...")
- 17:46, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 1/Examples/Zeta(4) over Zeta(8) (hist | edit) [1,054 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Sum of Reciprocals of Powers as Euler Product/Corollary 1 == <onlyinclude> {{begin-eqn}} {{eqn | l = \prod_{\text {$p$ prime} } \paren {1 + p^{-4} }...")
- 17:41, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 1/Examples/Zeta(2) over Zeta(4) (hist | edit) [1,043 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Sum of Reciprocals of Powers as Euler Product/Corollary 1 == <onlyinclude> {{begin-eqn}} {{eqn | l = \prod_{\text {$p$ prime} } \paren {1 + p^{-2} }...")
- 17:10, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 2/Examples (hist | edit) [799 bytes] Robkahn131 (talk | contribs) (Created page with "== Examples of Use of Sum of Reciprocals of Powers as Euler Product/Corollary 2 == <onlyinclude> === Sum of Reciprocals of Powers as Euler Product/Corollary 2/Examples/...")
- 17:01, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 2/Examples/Zeta^2(4) over Zeta(8) (hist | edit) [1,242 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Sum of Reciprocals of Powers as Euler Product/Corollary 2 == <onlyinclude> {{begin-eqn}} {{eqn | l = \prod_{\text {$p$ prime} } \paren {\frac {1 + p^...")
- 16:50, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 2/Examples/Zeta^2(2) over Zeta(4) (hist | edit) [1,202 bytes] Robkahn131 (talk | contribs) (Created page with "== Example of Use of Sum of Reciprocals of Powers as Euler Product/Corollary 2 == <onlyinclude> {{begin-eqn}} {{eqn | l = \prod_{\text {$p$ prime} } \paren {\frac {1 + p^...")
- 15:32, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 2 (hist | edit) [1,764 bytes] Robkahn131 (talk | contribs) (Created page with "== Corollary to Sum of Reciprocals of Powers as Euler Product == <onlyinclude> Let $\zeta$ be the Riemann zeta function. Let $s \in \...")
- 15:05, 4 March 2021 Sum of Reciprocals of Powers as Euler Product/Corollary 1 (hist | edit) [1,618 bytes] Robkahn131 (talk | contribs) (Created page with "== Corollary to Sum of Reciprocals of Powers as Euler Product == <onlyinclude> Let $\zeta$ be the Riemann zeta function. Let $s \in \...")
- 16:48, 3 March 2021 Area of Triangle in Determinant Form with Vertex at Origin/Proof 2 (hist | edit) [1,936 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Area of Triangle in Determinant Form == {{:Area of Triangle in Determinant Form with Vertex at Origin}} == Proof == <onlyinclude> Let the Definition:Polar...")
- 16:19, 3 March 2021 Area of Triangle in Determinant Form with Vertex at Origin/Proof 1 (hist | edit) [526 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Area of Triangle in Determinant Form == {{:Area of Triangle in Determinant Form with Vertex at Origin}} == Proof == <onlyinclude> {{begin-eqn}} {{eqn | l =...")
- 14:28, 3 March 2021 Conversion between Cartesian and Polar Coordinates in Plane/Examples/(-2, -pi over 4) (hist | edit) [1,794 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Use of Conversion between Cartesian and Polar Coordinates in Plane == <onlyinclude> The point $P$ defined in Definition:Polar Coordina...")
- 14:20, 3 March 2021 Conversion between Cartesian and Polar Coordinates in Plane/Examples/(4, pi over 3) (hist | edit) [1,738 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Use of Conversion between Cartesian and Polar Coordinates in Plane == <onlyinclude> The point $P$ defined in Definition:Polar Coordina...")
- 12:42, 3 March 2021 Distance between Two Points in Plane in Polar Coordinates/Proof 2 (hist | edit) [1,491 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Distance between Two Points in Plane in Polar Coordinates}} == Proof == <onlyinclude> From Conversion between Cartesian and Polar Coordinates in Plane, $...")
- 07:42, 3 March 2021 Distance between Two Points in Plane in Polar Coordinates/Proof 1 (hist | edit) [1,275 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Distance between Two Points in Plane in Polar Coordinates}} == Proof == <onlyinclude> Let $A$ and $B$ be embedded as suggested in a Definition:Polar Coordi...")
- 07:41, 3 March 2021 Conversion between Cartesian and Polar Coordinates in Plane/Examples (hist | edit) [639 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Conversion between Cartesian and Polar Coordinates in Plane == <onlyinclude> === Conversion between Cartesian and Polar Coordinates in Plane/Exampl...")
- 07:16, 3 March 2021 Distance between Two Points in Plane in Polar Coordinates (hist | edit) [1,189 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $A = \polar {r_1, \theta_1}$ and $B = \polar {r_2, \theta_2}$ be two points in a Definition:Polar Coordinate Plane|polar...")
- 20:53, 2 March 2021 Primitive of Root of a squared minus x squared/Mistake (hist | edit) [801 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|The Concise Oxford Dictionary of Mathematics|2014|Christopher Clapham|author2 = James Nicholson|ed = 5th|edpage = Fifth Edition}}: :Appendix...")
- 20:36, 2 March 2021 Primitive of Reciprocal of Root of x squared plus a squared/Mistake (hist | edit) [836 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|The Concise Oxford Dictionary of Mathematics|2014|Christopher Clapham|author2 = James Nicholson|ed = 5th|edpage = Fifth Edition}}: :Appendix...")
- 12:34, 2 March 2021 Primitive of Reciprocal/Mistake (hist | edit) [827 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Dictionary of Mathematics|1989|Ephraim J. Borowski|author2 = Jonathan M. Borwein}}: :'''Appendix $2$: Table of derivatives and integrals of...")
- 12:20, 2 March 2021 Derivative of Reciprocal (hist | edit) [862 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: \R_{\ne 0} \to \R$ be the reciprocal function defined as: :$\map f x = \dfrac 1 x$ Then its Definition:Derivative of Real...")
- 08:32, 2 March 2021 Binding Constraint/Examples/x^2 + y^2 le 2 (hist | edit) [671 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Binding Constraint == <onlyinclude> Consider the weak inequality: :$x^2 + y^2 \le 2$ Consider t...")
- 08:29, 2 March 2021 Binding Constraint/Examples (hist | edit) [256 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Binding Constraints == <onlyinclude> === Example: $x^2 + y^2 \le 2$ === {{:Bind...")
- 22:51, 1 March 2021 Legendre Symbol of Congruent Integers (hist | edit) [625 bytes] Caliburn (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $p$ be a odd prime. Let $a, b \in \Z$ be such that $a \equiv b \pmod p$. Then: :$\displaystyle \paren {\frac a p}...")