All public logs
Jump to navigation
Jump to search
Combined display of all available logs of Conformal Geometric Algebra. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 02:01, 13 April 2024 Eric Lengyel talk contribs created page Metrics (Created page with "The ''metric'' used in the 5D conformal geometric algebra over 3D Euclidean space is the $$5 \times 5$$ matrix $$\mathfrak g$$ given by :$$\mathfrak g = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 \\ 0 & 0 & 0 & -1 & 0\\\end{bmatrix}$$ . The ''metric exomorphism matrix'' $$\mathbf G$$, often just called the "metric" itself, corresponding to the metric $$\mathfrak g$$ is the $$32 \times 32$$ matrix shown below. Im...")
- 02:00, 13 April 2024 Eric Lengyel talk contribs created page File:Metric-cga-3d.svg
- 02:00, 13 April 2024 Eric Lengyel talk contribs uploaded File:Metric-cga-3d.svg
- 23:07, 3 April 2024 Eric Lengyel talk contribs deleted page File:AntiwedgeProduct.svg (Deleted old revision 20240403230709!AntiwedgeProduct.svg)
- 23:07, 3 April 2024 Eric Lengyel talk contribs uploaded a new version of File:AntiwedgeProduct.svg
- 23:06, 3 April 2024 Eric Lengyel talk contribs deleted page File:WedgeProduct.svg (Deleted old revision 20240403230647!WedgeProduct.svg)
- 23:06, 3 April 2024 Eric Lengyel talk contribs uploaded a new version of File:WedgeProduct.svg
- 23:05, 3 April 2024 Eric Lengyel talk contribs deleted page File:GeometricAntiproduct.svg (Deleted old revision 20240403230502!GeometricAntiproduct.svg)
- 23:05, 3 April 2024 Eric Lengyel talk contribs uploaded a new version of File:GeometricAntiproduct.svg
- 23:04, 3 April 2024 Eric Lengyel talk contribs deleted page File:GeometricProduct.svg (Deleted old revision 20240403230438!GeometricProduct.svg)
- 23:04, 3 April 2024 Eric Lengyel talk contribs uploaded a new version of File:GeometricProduct.svg
- 22:29, 31 December 2023 Eric Lengyel talk contribs created page Exterior product (Redirected page to Exterior products) Tag: New redirect
- 23:48, 1 December 2023 Eric Lengyel talk contribs created page Cocarriers (Redirected page to Carriers) Tag: New redirect
- 23:48, 1 December 2023 Eric Lengyel talk contribs deleted page Anticarrier (content was: "#REDIRECT Carriers", and the only contributor was "Eric Lengyel" (talk))
- 23:42, 1 December 2023 Eric Lengyel talk contribs created page Cocarrier (Redirected page to Carriers) Tag: New redirect
- 23:23, 1 December 2023 Eric Lengyel talk contribs deleted page File:Sphere.svg (Deleted old revision 20231201232345!Sphere.svg)
- 23:23, 1 December 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere.svg
- 23:23, 1 December 2023 Eric Lengyel talk contribs deleted page File:Circle.svg (Deleted old revision 20231201232332!Circle.svg)
- 23:23, 1 December 2023 Eric Lengyel talk contribs uploaded a new version of File:Circle.svg
- 23:23, 1 December 2023 Eric Lengyel talk contribs deleted page File:Dipole.svg (Deleted old revision 20231201232317!Dipole.svg)
- 23:23, 1 December 2023 Eric Lengyel talk contribs uploaded a new version of File:Dipole.svg
- 23:23, 1 December 2023 Eric Lengyel talk contribs deleted page File:Round.svg (Deleted old revision 20231201232258!Round.svg)
- 23:22, 1 December 2023 Eric Lengyel talk contribs uploaded a new version of File:Round.svg
- 06:59, 17 November 2023 Eric Lengyel talk contribs deleted page File:Plane.svg (Deleted old revision 20231117065936!Plane.svg)
- 06:59, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane.svg
- 06:59, 17 November 2023 Eric Lengyel talk contribs deleted page File:Line.svg (Deleted old revision 20231117065917!Line.svg)
- 06:59, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Line.svg
- 06:59, 17 November 2023 Eric Lengyel talk contribs deleted page File:Point.svg (Deleted old revision 20231117065901!Point.svg)
- 06:59, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Point.svg
- 06:47, 17 November 2023 Eric Lengyel talk contribs deleted page File:Sphere.svg (Deleted old revision 20231117064707!Sphere.svg)
- 06:47, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere.svg
- 06:46, 17 November 2023 Eric Lengyel talk contribs deleted page File:Circle.svg (Deleted old revision 20231117064650!Circle.svg)
- 06:46, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Circle.svg
- 06:46, 17 November 2023 Eric Lengyel talk contribs deleted page File:Dipole.svg (Deleted old revision 20231117064629!Dipole.svg)
- 06:46, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Dipole.svg
- 06:46, 17 November 2023 Eric Lengyel talk contribs deleted page File:Round.svg (Deleted old revision 20231117064604!Round.svg)
- 06:46, 17 November 2023 Eric Lengyel talk contribs uploaded a new version of File:Round.svg
- 03:23, 23 October 2023 Eric Lengyel talk contribs created page Antidual (Redirected page to Duals) Tag: New redirect
- 03:18, 23 October 2023 Eric Lengyel talk contribs created page Join (Redirected page to Join and meet) Tag: New redirect
- 03:18, 23 October 2023 Eric Lengyel talk contribs moved page Connect to Expansion without leaving a redirect
- 03:17, 23 October 2023 Eric Lengyel talk contribs created page Meet (Redirected page to Join and meet) Tag: New redirect
- 02:38, 23 October 2023 Eric Lengyel talk contribs deleted page File:Point connect round.svg (Deleted old revision 20231023023807!Point_connect_round.svg)
- 02:38, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Point connect round.svg
- 02:37, 23 October 2023 Eric Lengyel talk contribs deleted page File:Dipole connect round.svg (Deleted old revision 20231023023744!Dipole_connect_round.svg)
- 02:37, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Dipole connect round.svg
- 02:37, 23 October 2023 Eric Lengyel talk contribs deleted page File:Line connect dipole.svg (Deleted old revision 20231023023725!Line_connect_dipole.svg)
- 02:37, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Line connect dipole.svg
- 02:37, 23 October 2023 Eric Lengyel talk contribs deleted page File:Circle connect dipole.svg (Deleted old revision 20231023023710!Circle_connect_dipole.svg)
- 02:37, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Circle connect dipole.svg
- 02:36, 23 October 2023 Eric Lengyel talk contribs deleted page File:Line connect point.svg (Deleted old revision 20231023023654!Line_connect_point.svg)
- 02:36, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Line connect point.svg
- 02:36, 23 October 2023 Eric Lengyel talk contribs deleted page File:Circle connect point.svg (Deleted old revision 20231023023610!Circle_connect_point.svg)
- 02:36, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Circle connect point.svg
- 02:35, 23 October 2023 Eric Lengyel talk contribs deleted page File:Line connect round.svg (Deleted old revision 20231023023555!Line_connect_round.svg)
- 02:35, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Line connect round.svg
- 02:35, 23 October 2023 Eric Lengyel talk contribs deleted page File:Circle connect round.svg (Deleted old revision 20231023023533!Circle_connect_round.svg)
- 02:35, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Circle connect round.svg
- 02:35, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect line.svg (Deleted old revision 20231023023519!Plane_connect_line.svg)
- 02:35, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect line.svg
- 02:35, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect line.svg (Deleted old revision 20231023023503!Sphere_connect_line.svg)
- 02:35, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect line.svg
- 02:34, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect circle.svg (Deleted old revision 20231023023447!Plane_connect_circle.svg)
- 02:34, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect circle.svg
- 02:34, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect circle.svg (Deleted old revision 20231023023428!Sphere_connect_circle.svg)
- 02:34, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect circle.svg
- 02:34, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect point.svg (Deleted old revision 20231023023412!Plane_connect_point.svg)
- 02:34, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect point.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect point.svg (Deleted old revision 20231023023354!Sphere_connect_point.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect point.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect dipole.svg (Deleted old revision 20231023023339!Plane_connect_dipole.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect dipole.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect dipole.svg (Deleted old revision 20231023023321!Sphere_connect_dipole.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect dipole.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect round.svg (Deleted old revision 20231023023306!Plane_connect_round.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect round.svg
- 02:31, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect round.svg (Deleted old revision 20231023023140!Sphere_connect_round.svg)
- 02:31, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect round.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs created page File:AntiwedgeProduct.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs uploaded File:AntiwedgeProduct.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs created page File:WedgeProduct.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs uploaded File:WedgeProduct.svg
- 03:58, 6 August 2023 Eric Lengyel talk contribs created page Spheres (Redirected page to Sphere) Tag: New redirect
- 03:58, 6 August 2023 Eric Lengyel talk contribs created page Circles (Redirected page to Circle) Tag: New redirect
- 03:58, 6 August 2023 Eric Lengyel talk contribs created page Dipoles (Redirected page to Dipole) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Planes (Redirected page to Plane) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Lines (Redirected page to Line) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Flat points (Redirected page to Flat point) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Round points (Redirected page to Round point) Tag: New redirect
- 03:26, 6 August 2023 Eric Lengyel talk contribs created page Exterior antiproduct (Redirected page to Exterior products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Geometric antiproduct (Redirected page to Geometric products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Geometric product (Redirected page to Geometric products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Antiwedge product (Redirected page to Exterior products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Wedge product (Redirected page to Exterior products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Projection (Redirected page to Projections) Tag: New redirect
- 03:24, 6 August 2023 Eric Lengyel talk contribs created page Dual (Redirected page to Duals) Tag: New redirect
- 03:24, 6 August 2023 Eric Lengyel talk contribs created page Anticarrier (Redirected page to Carriers) Tag: New redirect
- 03:24, 6 August 2023 Eric Lengyel talk contribs created page Carrier (Redirected page to Carriers) Tag: New redirect
- 03:23, 6 August 2023 Eric Lengyel talk contribs created page Partner (Redirected page to Partners) Tag: New redirect
- 03:23, 6 August 2023 Eric Lengyel talk contribs created page Container (Redirected page to Containers) Tag: New redirect
- 03:20, 6 August 2023 Eric Lengyel talk contribs created page Transversion (Created page with "__NOTOC__ A ''transversion'' is a reciprocal transformation performed by the operator :$$\mathfrak T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{423} + \dfrac{\tau_y}{2} \mathbf e_{431} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{412} + \large\unicode{x1d7d9}}$$ . == Matrix Form == When a transversion $$\mathfrak T$$ is applied to a round point, it is equivalent to premultiplying the point by the $$5 \times 5$$ matrix :$$\begin{bmatrix} 1 & 0 & 0 & 0 & -\tau_x...")
- 03:20, 6 August 2023 Eric Lengyel talk contribs created page Dilation (Created page with "__NOTOC__ A ''dilation'' is a conformal transformation of Euclidean space performed by the operator :$$\mathbf D = \dfrac{1 - \sigma}{2} (c_x \mathbf e_{235} + c_y \mathbf e_{315} + c_z \mathbf e_{125} - \mathbf e_{321}) + \dfrac{1 + \sigma}{2} {\large\unicode{x1d7d9}}$$ . This operator scales an object $$\mathbf x$$ by the factor $$\sigma$$ about the center point $$\mathbf c = (c_x, c_y, c_z)$$ when used with the sandwich antiproduct $$\mathbf D \mathbin{\unicode{x27C...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Rotation (Created page with "__NOTOC__ A ''rotation'' is a proper isometry of Euclidean space performed by the operator :$$\mathbf R = \boldsymbol l\sin\dfrac{\phi}{2} + {\large\unicode{x1d7d9}}\cos\dfrac{\phi}{2}$$ , where $$\boldsymbol l$$ is a unitized line corresponding to the axis of rotation. This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Rotation rotation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It rotat...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Translation (Created page with "__NOTOC__ A ''translation'' is a proper isometry of Euclidean space performed by the operator :$$\mathbf T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{235} + \dfrac{\tau_y}{2} \mathbf e_{315} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{125} + \large\unicode{x1d7d9}}$$ . This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Translation translation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Projections (Created page with "Any geometric object $$\mathbf x$$ can be projected onto another geometric object $$\mathbf y$$ of higher grade by first calculating the connect of $$\mathbf x$$ with $$\mathbf y$$ and then using the meet operation to intersect the result with $$\mathbf y$$. That is, the projection of $$\mathbf x$$ onto $$\mathbf y$$ is given by :$$(\mathbf y^* \wedge \mathbf x) \vee \mathbf y$$ . This formula is general and works for flat points, lines, planes, r...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Connect (Created page with "The ''connect'' operation is performed by taking the wedge product between the dual of an object ''A'' and another object ''B'' with lower grade. The result is an object ''C'' that is orthogonal to ''A'' and contains ''B'', allowing a projection of ''B'' onto ''A'' through a simple intersection of ''A'' and ''C''. The flat points, lines, planes, round points, dipoles, circles, and spheres appearing in the following tables are defined...")
- 03:18, 6 August 2023 Eric Lengyel talk contribs created page Join and meet (Created page with "The ''join'' is a binary operation that calculates the higher-dimensional geometry containing its two operands, similar to a union. The ''meet'' is another binary operation that calculates the lower-dimensional geometry shared by its two operands, similar to an intersection. The flat points, lines, planes, round points, dipoles, circles, and spheres appearing in the following tables are defined as follows: :$$\mathbf p = p_x \mathbf e_{15} +...")
- 03:18, 6 August 2023 Eric Lengyel talk contribs created page Exterior products (Created page with "The ''exterior product'' is the fundamental product of Grassmann Algebra, and it forms part of the geometric product in geometric algebra. There are two products with symmetric properties called the exterior product and exterior antiproduct. == Exterior Product == The following Cayley table shows the exterior products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. 1440px == Exterior Anti...")
- 03:17, 6 August 2023 Eric Lengyel talk contribs created page Wedge products (Created page with "The ''exterior product'' is the fundamental product of Grassmann Algebra, and it forms part of the geometric product in geometric algebra. There are two products with symmetric properties called the exterior product and exterior antiproduct. == Exterior Product == The following Cayley table shows the exterior products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. 1440px == Exterior Anti...")
- 03:17, 6 August 2023 Eric Lengyel talk contribs created page Geometric products (Created page with "The ''geometric product'' is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct. == Geometric Product == The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the scalar basis element $$\mathbf 1$$. Cells colored yellow correspond...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Duals (Created page with "The ''dual'' of an object $$\mathbf x$$, denoted by $$\mathbf x^*$$, is given by :$$\mathbf x^* = \mathbf{\tilde x} \mathbin{\unicode{x27D1}} {\large\unicode{x1d7d9}}$$ . The following table lists the duals for the geometric objects in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. {| class="wikitable" ! Type !! Definition !! Dual |- | style="padding: 12px;" | Flat point | style="padding: 12px;" | $$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Attitude (Created page with "The ''attitude'' function, denoted by $$\operatorname{att}$$, extracts the attitude of a geometry and returns a purely directional object. The attitude function is defined as :$$\operatorname{att}(\mathbf x) = \mathbf x \vee \overline{\mathbf e_4}$$ . The following table lists the attitude for the geometric objects in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. {| class="wikitable" ! Type !! Definition !! Attitude |- | style="padding: 12px;" | Flat poin...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Partners (Created page with "The ''partner'' of a round object (a round point, dipole, circle, or sphere) is the round object having the same center, same carrier, and same absolute size, but having a squared radius of the opposite sign. The partner of an object $$\mathbf x$$ is denoted by $$\operatorname{par}(\mathbf x)$$, and it is given by the meet of the carrier of $$\mathbf x$$ with the container of $$\mathbf x^*$$: :$$\operatorname{par}(\mathbf x) = \operatorna...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Carriers (Created page with "== Carrier == The ''carrier'' of a round object (a round point, dipole, circle, or sphere) is the lowest dimensional flat object (a flat point, line, or plane) that contains it. The carrier of an object $$\mathbf x$$ is denoted by $$\operatorname{car}(\mathbf x)$$, and it is calculated by simply multiplying $$\mathbf x$$ by $$\mathbf e_5$$ with the wedge product to extract the round part of $$\mathbf x$$ as a flat geometry: :$$\operatorn...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Centers (Created page with "The ''center'' of a round object (a round point, dipole, circle, or sphere) is the round point having the same center and radius. The center of an object $$\mathbf x$$ is denoted by $$\operatorname{cen}(\mathbf x)$$, and it is given by the meet of $$\mathbf x$$ and its own anticarrier: :$$\operatorname{cen}(\mathbf x) = -\operatorname{car}(\mathbf x^*) \vee \mathbf x$$ . (The negative sign is not strictly necessary, but is included so the fu...")
- 03:15, 6 August 2023 Eric Lengyel talk contribs created page Containers (Created page with "The ''container'' of a round object (a round point, dipole, circle, or sphere) is the smallest sphere that contains it. The container of an object $$\mathbf x$$ is denoted by $$\operatorname{con}(\mathbf x)$$, and it is given by the connect of $$\mathbf x$$ with its own carrier: :$$\operatorname{con}(\mathbf x) = \operatorname{car}(\mathbf x)^* \wedge \mathbf x$$ . The squared radius of an object's container has the same sign as the squared radi...")
- 03:15, 6 August 2023 Eric Lengyel talk contribs created page Center (Created page with "The ''center'' of a round object (a round point, dipole, circle, or sphere) is the round point having the same center and radius. The center of an object $$\mathbf x$$ is denoted by $$\operatorname{cen}(\mathbf x)$$, and it is given by the meet of $$\mathbf x$$ and its own anticarrier: :$$\operatorname{cen}(\mathbf x) = -\operatorname{car}(\mathbf x^*) \vee \mathbf x$$ . (The negative sign is not strictly necessary, but is included so the fu...")
- 03:15, 6 August 2023 Eric Lengyel talk contribs created page Sphere (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''sphere'' $$\mathbf s$$ is a quadrivector having the general form :$$\mathbf s = s_u \mathbf e_{1234} + s_x \mathbf e_{4235} + s_y \mathbf e_{4315} + s_z \mathbf e_{4125} + s_w \mathbf e_{3215}$$ . If the $$s_u$$ component is zero, then the sphere contains the point at infinity, and it is thus a flat plane. Given a center $$\mathbf p = (p_x, p_y, p_z)$$ and a radius $$r$$, a sphere can be...")
- 03:15, 6 August 2023 Eric Lengyel talk contribs created page Circle (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''circle'' $$\mathbf c$$ is a trivector with ten components having the general form :$$\mathbf c = c_{gx} \mathbf e_{423} + c_{gy} \mathbf e_{431} + c_{gz} \mathbf e_{412} + c_{gw} \mathbf e_{321} + c_{vx} \mathbf e_{415} + c_{vy} \mathbf e_{425} + c_{vz} \mathbf e_{435} + c_{mx} \mathbf e_{235} + c_{my} \mathbf e_{315} + c_{mz} \mathbf e_{125}$$ . If the $$gx$$, $$gy$$, $$gz$$, and $$gw$$ componen...")
- 03:14, 6 August 2023 Eric Lengyel talk contribs created page Dipole (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''dipole'' $$\mathbf d$$ is a bivector with ten components having the general form :$$\mathbf d = d_{vx} \mathbf e_{41} + d_{vy} \mathbf e_{42} + d_{vz} \mathbf e_{43} + d_{mx} \mathbf e_{23} + d_{my} \mathbf e_{31} + d_{mz} \mathbf e_{12} + d_{px} \mathbf e_{15} + d_{py} \mathbf e_{25} + d_{pz} \mathbf e_{35} + d_{pw} \mathbf e_{45}$$ . If the $$vx$$, $$vy$$, $$vz$$, $$mx$$, $$my$$, and $$mz$$ com...")
- 03:14, 6 August 2023 Eric Lengyel talk contribs created page Round point (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''round point'' $$\mathbf a$$ is a vector having the general form :$$\mathbf a = a_x \mathbf e_1 + a_y \mathbf e_2 + a_z \mathbf e_3 + a_w \mathbf e_4 + a_u \mathbf e_5$$ . Given a position $$\mathbf p = (p_x, p_y, p_z)$$ and a radius $$r$$, a round point can be formulated as :$$\mathbf a = p_x \mathbf e_1 + p_y \mathbf e_2 + p_z \mathbf e_3 + \mathbf e_4 + \dfrac{p^2 + r^2}{2} \mathbf e_5$$ . Th...")
- 03:14, 6 August 2023 Eric Lengyel talk contribs created page Plane (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a plane. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''plane'' $$\mathbf g$$ is a quadrivector having the general form :$$\mathbf g = g_x \mathbf e_{4235} + g_y \mathbf e_{4315} + g_z \mathbf e_{4125} + g_w \mathbf e_{3215}$$ . A plane can be viewed as an infinitely large sphere containing the point at infinity. A plane in conformal geometric algebra is the precise...")
- 03:14, 6 August 2023 Eric Lengyel talk contribs created page Line (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a line. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''line'' $$\boldsymbol l$$ is a trivector having the general form :$$\boldsymbol l = v_x \mathbf e_{415} + v_y \mathbf e_{425} + v_z \mathbf e_{435} + m_x \mathbf e_{235} + m_y \mathbf e_{315} + m_z \mathbf e_{125}$$ . A line can be viewed as an infinitely large circle that contains the point at infinity. A line in...")
- 03:13, 6 August 2023 Eric Lengyel talk contribs created page Flat point (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a flat point. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''flat point'' $$\mathbf p$$ is a bivector having the general form :$$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p_z \mathbf e_{35} + p_w \mathbf e_{45}$$ . A flat point can be viewed as a dipole that has one end at the point at infinity. A flat point in conformal geometric algebra is the precise...")
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Wedge product.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Wedge product.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet sphere.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet sphere.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet plane.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet plane.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Round join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Round join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Point join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Point join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Point connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Point connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane meet plane.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane meet plane.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane meet line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane meet line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane meet dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane meet dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane meet circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane meet circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane connect line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane connect line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:GeometricProduct.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:GeometricProduct.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane connect circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane connect circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Line join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Line join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:GeometricAntiproduct.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:GeometricAntiproduct.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Line connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Line connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Line connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Line connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Line connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Line connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Horosphere.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Horosphere.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Dipole join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Dipole join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Dipole join point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Dipole join point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Dipole join dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Dipole join dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Dipole connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Dipole connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle meet line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle meet line.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle meet circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle meet circle.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle join round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Antiwedge product.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Antiwedge product.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle connect round.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Circle connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle connect point.svg (Uploaded with SimpleBatchUpload)
- 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Circle connect dipole.svg (Uploaded with SimpleBatchUpload)
- 03:07, 6 August 2023 MediaWiki default talk contribs created page Main Page