User contributions for Telliott99
Jump to navigation
Jump to search
7 December 2023
- 17:4817:48, 7 December 2023 diff hist +7,840 N Pappus's Hexagon Theorem/Proof 1 Created page with "== Theorem == {{:Pappus's Hexagon Theorem}} == Proof == <onlyinclude> 300px The notation has been changed to match the source. Let $ACE$ be collinear and $BFD$ also be collinear. Join $ABCDEF$ in order. The points where opposite sides of the hexagon cut each other are $NLM$: * $AB$ and $DE$ cro..."
6 December 2023
- 20:3520:35, 6 December 2023 diff hist +58 N File:PappusHexagonTheorem-3.png No edit summary current
- 20:3320:33, 6 December 2023 diff hist +43 N File:PappusHexagonTheorem-1.png No edit summary current
5 December 2023
- 22:4922:49, 5 December 2023 diff hist 0 m Steiner-Lehmus Theorem/Proof 3 No edit summary current
29 November 2023
- 01:5101:51, 29 November 2023 diff hist +229 Talk:Archimedes' Limits to Value of Pi No edit summary
- 00:1900:19, 29 November 2023 diff hist −943 Talk:Archimedes' Limits to Value of Pi No edit summary Tag: Manual revert
- 00:1800:18, 29 November 2023 diff hist −131 Archimedes' Limits to Value of Pi No edit summary Tag: Manual revert
28 November 2023
- 23:1923:19, 28 November 2023 diff hist +108 Archimedes' Limits to Value of Pi No edit summary
- 23:1923:19, 28 November 2023 diff hist +775 N Archimedes' Limits to Value of Pi/Archimedes' Iterative Proof/Historical Note Created page with "== Comment on Archimedes' Limits to Value of Pi == <onlyinclude> The upper bound analysis starts by finding the perimeter of a circumscribed hexagon. Symmetry gives one side as twice the tangent of a right triangle with central angle $30 \degrees$ in a unit circle. The lower bound analysis starts by finding the perimeter of an inscribed hexagon as the sine of a right triangle with inscribed angle of $60 \degrees$ in a circle with unit diameter. Although the two..."
- 13:2413:24, 28 November 2023 diff hist +943 Talk:Archimedes' Limits to Value of Pi No edit summary
27 November 2023
- 17:5817:58, 27 November 2023 diff hist +43 N File:PappusHexagonTheorem-2.png No edit summary current
- 14:3014:30, 27 November 2023 diff hist −56 m Triangle Right-Angle-Hypotenuse-Side Congruence/Proof 2 No edit summary
- 12:1612:16, 27 November 2023 diff hist −190 Equiangular Right Triangles are Similar/Proof 2 No edit summary current
26 November 2023
- 22:4822:48, 26 November 2023 diff hist +898 Position of Centroid of Triangle on Median/Proof 3 No edit summary
- 20:3220:32, 26 November 2023 diff hist +3,169 N Medians of Triangle Form Six Triangles of Equal Area Created page with "== Theorem == <onlyinclude> :500px Let $\triangle ABC$ be an arbitrary triangle. Draw $AL$, $BM$ and $CN$, the medians of $\triangle ABC$. Then $\triangle ABC$ is divided into six small triangles: * $\triangle GAN$ * $\triangle GBN$ * $\triangle GBL$ * $\triangle GCL$ * $\triangle GCM$ * $\triangle GAM$ Each one of these six Defini..." current
- 20:2520:25, 26 November 2023 diff hist +1,694 N Position of Centroid of Triangle on Median/Proof 3 Created page with "These two triangles have their bases on the median $AGL$ and share vertex $C$: * $\triangle CGA$ * $\triangle CGL$ Thus, the two triangles have the same altitude. By Areas of Triangles and Parallelograms Proportional to Base: :$\dfrac { \AA \paren { \triangle CGA } } { \AA \paren { \triangle CGL..."
25 November 2023
- 21:4121:41, 25 November 2023 diff hist +82 Broken Chord Theorem No edit summary current
- 21:4021:40, 25 November 2023 diff hist +1,735 N Broken Chord Theorem/Proof 5 Created page with "== Theorem == {{:Broken Chord Theorem}} == Proof == <onlyinclude> 300px Given $MD \perp BC$ Draw $MN \parallel BC$ to meet the circle at $N$. Draw $NE \parallel MD$. By Quadrilateral is Parallelogram iff Both Pairs of Opposite Sides are Equal or Parallel: :$MNED$ is a parallelogram By Parallelogram with One Right Angle is Rectangle: :$MNED$ is a rectangle. {{begin-eqn}}..."
- 21:3021:30, 25 November 2023 diff hist +40 N File:BrokenChordTheorem-5.png No edit summary current
- 21:1421:14, 25 November 2023 diff hist +82 Broken Chord Theorem No edit summary
- 21:1221:12, 25 November 2023 diff hist +1,966 N Broken Chord Theorem/Proof 4 Created page with "== Theorem == {{:Broken Chord Theorem}} == Proof == <onlyinclude> Find $E$ on $BC$ such that $BD = BE$. 400px {{begin-eqn}} {{eqn | l = BD | r = ED | c = {{hypothesis}} }} {{eqn | l = MD | o = \perp | r = BE | c = {{hypothesis}} }} {{eqn | l = \triangle MBD | o = \cong | r = \triangle MED | c = Triangle Side-Angle-Side Congruence }} {{eqn | ll = \leadsto | l = MB | r = ME..."
- 16:2016:20, 25 November 2023 diff hist +283 N Talk:Orthocenter, Centroid and Circumcenter Coincide iff Triangle is Equilateral Created page with "Wonder what is seen as clumsy. I can make it simpler but not shorter (12 statements). Is it the use of Altitude, Median and Perpendicular Bisector Coincide iff Triangle is Isosceles? --~~~~" current
- 13:0213:02, 25 November 2023 diff hist +5 Area of Triangle in Terms of Side and Altitude No edit summary
- 10:4610:46, 25 November 2023 diff hist −34 Position of Centroid of Triangle on Median/Proof 2 No edit summary
- 10:4610:46, 25 November 2023 diff hist +2,019 N Position of Centroid of Triangle on Median/Proof 2 Created page with "== Theorem == {{:Position of Centroid of Triangle on Median}} == Proof == <onlyinclude> :400px Let $\triangle ABC$ be a triangle. Let $AL$, $BM$ and $CN$ be the medians of $\triangle ABC$. Let the medians be concurrent at the centroid, $P$. By the definition of Definition:Median of Trian..."
24 November 2023
- 23:3023:30, 24 November 2023 diff hist +39 N File:Broken Chord 4.png No edit summary current
- 14:4914:49, 24 November 2023 diff hist −41 Ceva's Theorem/Proof 2 No edit summary
- 14:0214:02, 24 November 2023 diff hist +70 Ceva's Theorem No edit summary
- 14:0014:00, 24 November 2023 diff hist +3,072 N Ceva's Theorem/Proof 2 Created page with "== Theorem == {{:Ceva's Theorem}} == Proof == <onlyinclude> === Necessary Condition === {{hypothesis}}: :$AL$, $BM$ and $CN$ are concurrent in $\triangle ABC$ at point $P$. :400px Following the sides anticlockwise in $\triangle LAB$: {{begin-eqn}} {{eqn | n = 1 | l = \dfrac {LP} {PA} \cdot \dfrac {AN} {NB} \cdot \dfrac {BC} {CL} |..."
23 November 2023
- 19:3319:33, 23 November 2023 diff hist +35 Euler Triangle Formula/Proof 2 No edit summary
- 12:1412:14, 23 November 2023 diff hist +279 Euler Triangle Formula/Lemma 2/Proof 2 No edit summary current
22 November 2023
- 22:1922:19, 22 November 2023 diff hist −975 Euler Triangle Formula/Lemma 2 No edit summary
- 22:1722:17, 22 November 2023 diff hist +161 N Talk:Euler Triangle Formula/Lemma 2/Proof 1 Created page with "I messed up. Should be Euler's Triangle Formula/Lemma 2/Proof 1. --~~~~"
- 22:1522:15, 22 November 2023 diff hist +1,316 N Euler Triangle Formula/Lemma 2/Proof 1 Created page with "=== Lemma 2 === {{:Euler Triangle Formula/Lemma 2}}{{qed|lemma}} == Proof == {{WLOG}}, it will be demonstrated that $BP = IP$. Let $CP$ be the bisector of $\angle ACB$. :$\angle ACP$ and $\angle ICB$ both subtend $AP$. Hence indirectly by the Inscribed Angle Theorem: :$\angle ACP = \angle ICB$ From Angles on Equal Arcs are Equal: :$\angle ACP = \angle ABP$ and so: :$\angle ABP = \angle ICB$ By the..."
- 21:5721:57, 22 November 2023 diff hist +211 N Talk:Euler Triangle Formula Created page with "I still need to explain your area figure, and I have a new short proof of Lemma 2 which needs to be properly linked. --~~~~" current
- 21:4321:43, 22 November 2023 diff hist +1,232 N Euler Triangle Formula/Lemma 2/Proof 2 Created page with "== Lemma to Euler Triangle Formula == <onlyinclude> :400px Let the bisector of angle $C$ of triangle $\triangle ABC$ be produced to the circumcircle at $P$. Let $I$ be the incenter of $\triangle ABC$. Then: :$AP = BP = IP$ </onlyinclude>..."
- 21:4121:41, 22 November 2023 diff hist +50 N File:EulerTriangleLemma-2a.png No edit summary current
- 21:0921:09, 22 November 2023 diff hist +318 Talk:Euler Triangle Formula/Proof 2 No edit summary
- 21:0521:05, 22 November 2023 diff hist −951 Euler Triangle Formula/Proof 2 No edit summary
- 20:5320:53, 22 November 2023 diff hist −693 Euler Triangle Formula/Proof 1 No edit summary
- 20:4920:49, 22 November 2023 diff hist +1,285 N Euler Triangle Formula/Lemma 1 Created page with "== Lemma to Euler Triangle Formula == <onlyinclude> :400px Let the incenter of $\triangle ABC$ be $I$. Let the circumcenter of $\triangle ABC$ be $O$. Let $OI$ be produced to the circumcircle at $G$ and $J$. Let $CI$ be produced to the Definition:Circum..."
- 16:1816:18, 22 November 2023 diff hist +236 N Talk:Euler Triangle Formula/Proof 2 Created page with "This replaces only the second half of Proof 1. So probably both should be refactored with a second Lemma shared between Proof 1 and Proof 2. --~~~~"
- 16:0916:09, 22 November 2023 diff hist −11 m Euler Triangle Formula/Proof 2 No edit summary
- 16:0716:07, 22 November 2023 diff hist +2,822 N Euler Triangle Formula/Proof 2 Created page with "Euler Triangle Formula/Proof 2 == Theorem == {{:Euler Triangle Formula}} == Proof == <onlyinclude> 400px == Proof == === Lemma === {{:Euler Triangle Formula/Lemma}} {{qed|lemma}} :400px Let the incenter of $\triangle ABC$ be $I$. Let the circumcenter of $\triangle ABC$..."
- 16:0416:04, 22 November 2023 diff hist 0 Euler Triangle Formula No edit summary
- 16:0316:03, 22 November 2023 diff hist −2,027 Euler Triangle Formula No edit summary
- 16:0116:01, 22 November 2023 diff hist +2,368 N Euler Triangle Formula/Proof 1 Created page with "== Theorem == {{:Euler Triangle Formula}} == Proof == <onlyinclude> === Lemma === {{:Euler Triangle Formula/Lemma}} {{qed|lemma}} :400px Let the incenter of $\triangle ABC$ be $I$. Let the circumcenter of $\triangle ABC$ be $O$. Let $OI$ be produced to the Definition:Circumcircle of Tria..."
- 13:4913:49, 22 November 2023 diff hist +265 Menelaus's Theorem No edit summary current
- 12:3512:35, 22 November 2023 diff hist +59 N File:Pascal's Theorem.png No edit summary current
21 November 2023
- 23:0923:09, 21 November 2023 diff hist +43 N File:Incenter Circumcenter Distance 2.png No edit summary current