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Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 17:48, 7 December 2023 Telliott99 talk contribs created page 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...")
- 20:35, 6 December 2023 Telliott99 talk contribs created page File:PappusHexagonTheorem-3.png
- 20:35, 6 December 2023 Telliott99 talk contribs uploaded File:PappusHexagonTheorem-3.png
- 20:33, 6 December 2023 Telliott99 talk contribs created page File:PappusHexagonTheorem-1.png
- 20:33, 6 December 2023 Telliott99 talk contribs uploaded File:PappusHexagonTheorem-1.png
- 23:19, 28 November 2023 Telliott99 talk contribs created page Archimedes' Limits to Value of Pi/Comment (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...")
- 17:58, 27 November 2023 Telliott99 talk contribs uploaded File:PappusHexagonTheorem-2.png
- 17:58, 27 November 2023 Telliott99 talk contribs created page File:PappusHexagonTheorem-2.png
- 20:32, 26 November 2023 Telliott99 talk contribs created page 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...")
- 20:25, 26 November 2023 Telliott99 talk contribs created page Position of Centroid 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...")
- 21:40, 25 November 2023 Telliott99 talk contribs created page 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}}...")
- 21:30, 25 November 2023 Telliott99 talk contribs uploaded File:BrokenChordTheorem-5.png
- 21:30, 25 November 2023 Telliott99 talk contribs created page File:BrokenChordTheorem-5.png
- 21:12, 25 November 2023 Telliott99 talk contribs created page 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...")
- 16:20, 25 November 2023 Telliott99 talk contribs created page 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? --~~~~")
- 10:46, 25 November 2023 Telliott99 talk contribs created page 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...")
- 23:30, 24 November 2023 Telliott99 talk contribs uploaded File:Broken Chord 4.png
- 23:30, 24 November 2023 Telliott99 talk contribs created page File:Broken Chord 4.png
- 14:03, 24 November 2023 Telliott99 talk contribs created page Talk:Ceva's Theorem (Created page with "Sorry, but I do not know how to deal with the necessary refactoring b/c of Sources. --~~~~")
- 14:00, 24 November 2023 Telliott99 talk contribs created page 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} |...")
- 22:17, 22 November 2023 Telliott99 talk contribs created page Talk:Euler's Triangle Formula/Lemma 1/ Proof 1 (Created page with "I messed up. Should be Euler's Triangle Formula/Lemma 2/Proof 1. --~~~~")
- 22:15, 22 November 2023 Telliott99 talk contribs created page Euler's Triangle Formula/Lemma 1/ 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...")
- 21:57, 22 November 2023 Telliott99 talk contribs created page 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. --~~~~")
- 21:43, 22 November 2023 Telliott99 talk contribs created page 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>...")
- 21:41, 22 November 2023 Telliott99 talk contribs uploaded File:EulerTriangleLemma-2a.png
- 21:41, 22 November 2023 Telliott99 talk contribs created page File:EulerTriangleLemma-2a.png
- 20:49, 22 November 2023 Telliott99 talk contribs created page 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...")
- 16:18, 22 November 2023 Telliott99 talk contribs created page 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. --~~~~")
- 16:07, 22 November 2023 Telliott99 talk contribs created page 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 $\triangle ABC$...")
- 16:01, 22 November 2023 Telliott99 talk contribs created page 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...")
- 12:35, 22 November 2023 Telliott99 talk contribs uploaded File:Pascal's Theorem.png
- 12:35, 22 November 2023 Telliott99 talk contribs created page File:Pascal's Theorem.png
- 23:09, 21 November 2023 Telliott99 talk contribs uploaded File:Incenter Circumcenter Distance 2.png
- 23:09, 21 November 2023 Telliott99 talk contribs created page File:Incenter Circumcenter Distance 2.png
- 19:59, 20 November 2023 Telliott99 talk contribs created page Phi in the Pentagon (Created page with "Phi in the Pentagon == Theorem == <onlyinclude> Let $ABCDE$ be a regular pentagon. The chords and sides of $ABCDE$ form three kinds of similar triangles. * I: Isosceles, similar to $\triangle ACD$. * II: Isosceles, Definition:Similar Triang...")
- 19:43, 20 November 2023 Telliott99 talk contribs uploaded File:PhiPentagon.png
- 19:43, 20 November 2023 Telliott99 talk contribs created page File:PhiPentagon.png
- 15:19, 19 November 2023 Telliott99 talk contribs created page Parallelogram with One Right Angle is Rectangle (Created page with "== Theorem == <onlyinclude> Let $\Box ABCD$ be a parallelogram. Let one angle of $\Box ABCD$ be a right angle. Then $\Box ABCD$ is a rectangle. </onlyinclude> == Proof == {{WLOG}}, let $\angle ABC$ be a right angle. Let $\angle CDA$ be opposite $\angle ABC$. By Opposite Sides and Angles of Parallel...")
- 14:41, 19 November 2023 Telliott99 talk contribs uploaded File:9PointCircleLabels.png
- 14:41, 19 November 2023 Telliott99 talk contribs created page File:9PointCircleLabels.png
- 17:16, 17 November 2023 Telliott99 talk contribs created page Steiner-Lehmus Theorem/Proof 4 (Created page with "== Theorem == {{:Steiner-Lehmus Theorem}} == Proof == <onlyinclude> === {{Lemma|Steiner-Lehmust Theorem|1}} === {{:Steiner-Lehmust Theorem/Lemma 1}} === {{Lemma|Steiner-Lehmust Theorem|2}} === {{:Steiner-Lehmust Theorem/Lemma 2}} 400px Let $\triangle ABC$ be a triangle. Let $\angle ABC$ be bisected by $BM$ Let $\angle ACB$ be bisected by $CN$. Let $BM = CN$. S...")
- 17:09, 17 November 2023 Telliott99 talk contribs created page Steiner-Lehmus Theorem/Lemma 2 (Created page with "=== Lemma for Steiner-Lehmus Theorem === <onlyinclude> Let $\triangle ABC$ be a triangle. Let $\angle ABC$ be bisected by $BM$. Let $\angle ACB$ be bisected by $CN$. Let $\angle ABC < \angle ACB$. Then $CN < BM$. </onlyinclude> === Proof === 300px Let $\angle NBM = \angle MBC = \beta$. Let $\angle NCB = \angle NCM = \gamma$. {{hypothesis}} :$\angle ABC <...")
- 17:06, 17 November 2023 Telliott99 talk contribs uploaded File:Steiner-Lehmus Proof 4.png
- 17:06, 17 November 2023 Telliott99 talk contribs created page File:Steiner-Lehmus Proof 4.png
- 17:04, 17 November 2023 Telliott99 talk contribs created page Steiner-Lehmus Theorem/Lemma 1 (Created page with "=== Lemma for Steiner-Lehmus Theorem === <onlyinclude> In the same circle, the larger chord subtends the larger angle. </onlyinclude> === Proof === Let there be a circle on center $O$. Let $PQ$ and $PR$ be two chords on the circle from the same point $P$. Let [...")
- 18:12, 16 November 2023 Telliott99 talk contribs created page Talk:Addition of Inequalities (Created page with "I hope it's clear that I did not know about the other entry. This is essentially the same proof, except the existing one used trichotomy rather than transitivity. Can you please leave this page and just redirect? It would be nice if search terms like "Add Inequalities" or "Addition of Inequalities" returned meaningful results. --~~~~")
- 13:41, 16 November 2023 Telliott99 talk contribs created page Addition of Inequalities (Created page with "== Theorem == <onlyinclude> Let $a$, $b$, $c$ and $d$ be real numbers. Let $a > b$. Let $c > d$. Then $a + c > b + d$. == Proof == {{begin-eqn}} {{eqn | l = a | o = > | r = b | c = {{hypothesis}} }} {{eqn | l = a + c | o = > | r = b + c | c = Real Number Ordering is Compatible with Addition }} {{eqn | l = c | o = > | r = d | c = {{hypothesis}} }} {{eqn | l = b + c | o = >...")
- 01:21, 16 November 2023 Telliott99 talk contribs created page Talk:Power of Point equals Product of Lengths of Line Segments to Circumference (Created page with "The reason the lengths are directed is so that $PA \cdot PA'$ matches the definition of Power of Point everywhere. Namely, negative inside and positive outside the circle, and zero on the circle as well. --~~~~")
- 23:43, 15 November 2023 Telliott99 talk contribs created page Power of Point (Created page with "== Theorem == <onlyinclude> Let $C$ be a circle in the plane on center $O$ with radius $r$. Let $P$ be an arbitrary point. Let a directed line segment from $P$ be drawn cutting $C$ at $A$ and $A'$, or meeting $C$ at $A = A'$, for a tangent. Let $p$ be the Definition:Power of Point...")
- 18:16, 15 November 2023 Telliott99 talk contribs uploaded File:Power of Point Interior.png