From c52a4b60576052f52f12345c9d3820206972dafa Mon Sep 17 00:00:00 2001 From: Aron T Date: Tue, 7 Oct 2025 17:43:15 +0300 Subject: [PATCH 1/5] Add SVG diagrams for triangle types by side and angle MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Added diagram 1: Triangle types by side length (equilateral, isosceles, scalene) - All triangles have base at bottom - Equilateral has perpendicular tick marks on all three sides - Isosceles has double tick marks on two equal sides - Scalene has labeled sides a, b, c - Added diagram 2: Triangle types by angle measure (acute, right, obtuse) - Acute triangle shows three 60° angles with concave arcs - Right triangle shows 90° angle with square symbol, two 45° angles - Obtuse triangle shows 120° obtuse angle and two acute angles (40°, 20°) - All angle arcs are properly concave and touch triangle sides - All labels are carefully positioned for clarity --- docs/src/Geometry/01 Triangles.md | 128 ++++++++++++++++++++++++++++++ 1 file changed, 128 insertions(+) diff --git a/docs/src/Geometry/01 Triangles.md b/docs/src/Geometry/01 Triangles.md index 0c98345..b51dc3e 100644 --- a/docs/src/Geometry/01 Triangles.md +++ b/docs/src/Geometry/01 Triangles.md @@ -10,12 +10,140 @@ - **[Isosceles](https://mathworld.wolfram.com/IsoscelesTriangle.html):** Two sides equal - **[Scalene](https://mathworld.wolfram.com/ScaleneTriangle.html):** All sides different +```@raw html + + + + + + + + + + + + + + + + Equilateral + (all sides equal) + + + + + + + + + + + + + + + + + Isosceles + (two sides equal) + + + + + + + + + a + b + c + + + Scalene + (all sides different) + + +``` + ### By Angle Measure - **[Acute](https://mathworld.wolfram.com/AcuteTriangle.html):** All angles less than 90° - **[Right](https://mathworld.wolfram.com/RightTriangle.html):** One angle equals 90° - **[Obtuse](https://mathworld.wolfram.com/ObtuseTriangle.html):** One angle greater than 90° +```@raw html + + + + + + + + + + 60° + + + + 60° + + + + 60° + + + Acute + (all angles < 90°) + + + + + + + + + + 90° + + + + + 45° + + + + 45° + + + Right + (one angle = 90°) + + + + + + + + + + 120° + + + + + 40° + + + + 20° + + + Obtuse + (one angle > 90°) + + +``` + ## Triangle Properties ### Fundamental Properties of Triangles From a9941b65c8a45b1582c4cffe624431e50746ae06 Mon Sep 17 00:00:00 2001 From: Aron T Date: Sun, 12 Oct 2025 18:13:51 +0300 Subject: [PATCH 2/5] Add SVG diagram for cevians (median, altitude, angle bisector) - Added diagram 4: Three triangles showing different cevian types - Median: Blue dashed line from vertex to midpoint with equal segment marks - Altitude: Red dashed line perpendicular to base with right angle symbol - Angle bisector: Purple dashed line with equal angle arcs at vertex - All cevians properly positioned with clear visual markers - Updated TODO to remove completed diagram 4 --- docs/src/Geometry/01 Triangles.md | 75 +++++++++++++++++++++++++++++++ 1 file changed, 75 insertions(+) diff --git a/docs/src/Geometry/01 Triangles.md b/docs/src/Geometry/01 Triangles.md index b51dc3e..f2d9ba8 100644 --- a/docs/src/Geometry/01 Triangles.md +++ b/docs/src/Geometry/01 Triangles.md @@ -2,6 +2,18 @@ [Triangles](https://mathworld.wolfram.com/Triangle.html) are three-sided polygons that form the foundation of much geometric and trigonometric study. + + ## Types of Triangles ### By Side Length @@ -178,6 +190,69 @@ A [cevian](https://mathworld.wolfram.com/Cevian.html) is a line segment that joi - **[Altitude](https://mathworld.wolfram.com/Altitude.html):** Cevian perpendicular to opposite side - **[Angle bisector](https://mathworld.wolfram.com/AngleBisector.html):** Cevian that bisects the angle at a vertex +```@raw html + + + + + + + + + + + + M (midpoint) + + + + + + + Median + + + + + + + + + + + + + + + + H (foot) + + + Altitude + + + + + + + + + + + + + + + + + D + + + Angle Bisector + + +``` + ### Ceva's Theorem [Giovanni Ceva](https://en.wikipedia.org/wiki/Giovanni_Ceva) (1647-1734) was an Italian mathematician who discovered this fundamental theorem about concurrent cevians. His work laid important groundwork for projective geometry and triangle geometry. From e90e5ba27b4c42fa83155a340d20f704bfbbdd30 Mon Sep 17 00:00:00 2001 From: Aron T Date: Tue, 14 Oct 2025 16:42:55 +0300 Subject: [PATCH 3/5] Add SVG diagrams for all four triangle centers - Circumcenter: perpendicular bisectors of sides meeting at center, circumcircle passing through all vertices, tick marks showing bisected sides, right angle symbols positioned inside triangle - Incenter: angle bisectors meeting at center, incircle tangent to all sides and fitting inside triangle - Centroid: medians from vertices to opposite midpoints converging at center, tick marks showing bisected sides - Orthocenter: altitudes from vertices perpendicular to opposite sides intersecting at orthocenter All four centers displayed in single 800x280 SVG with proper geometric positioning and visual markers. Updated TODO list to reflect completion. --- docs/src/Geometry/01 Triangles.md | 147 ++++++++++++++++++++++++++++-- 1 file changed, 141 insertions(+), 6 deletions(-) diff --git a/docs/src/Geometry/01 Triangles.md b/docs/src/Geometry/01 Triangles.md index f2d9ba8..3de6a17 100644 --- a/docs/src/Geometry/01 Triangles.md +++ b/docs/src/Geometry/01 Triangles.md @@ -3,11 +3,6 @@ [Triangles](https://mathworld.wolfram.com/Triangle.html) are three-sided polygons that form the foundation of much geometric and trigonometric study. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + O + + + + + + Circumcircle/Circumcenter + + + + + + + + + + + + + + + + + + I + + + + + + Incenter + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + G + + + Centroid + + + + + + + + + + + + + + + + + + H + + + Orthocenter + + +``` + ## Area Calculations ### Standard Formula From dee9bb4c47a59963496a3b833ee2e6e3cde7ebe9 Mon Sep 17 00:00:00 2001 From: Aron T Date: Wed, 22 Oct 2025 14:38:49 +0300 Subject: [PATCH 4/5] Add SVG diagram for Pythagorean theorem MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Right triangle with three squares showing a² + b² = c² - Blue square on vertical leg (a²) - Green square on horizontal leg (b²) - Red square on hypotenuse (c²), rotated 45° to align with hypotenuse - Formula displayed at top of diagram - Right angle indicator at 90° corner - Centered diagram with proper alignment of all squares - SVG wrapped in centered div for better presentation --- docs/src/Geometry/01 Triangles.md | 36 +++++++++++++++++++++++++++++++ 1 file changed, 36 insertions(+) diff --git a/docs/src/Geometry/01 Triangles.md b/docs/src/Geometry/01 Triangles.md index 3de6a17..7971407 100644 --- a/docs/src/Geometry/01 Triangles.md +++ b/docs/src/Geometry/01 Triangles.md @@ -448,6 +448,42 @@ Right triangles have special properties and are fundamental to trigonometry. - **[Right Triangle](https://mathworld.wolfram.com/RightTriangle.html):** A triangle with one angle equal to 90°. - **[Cathetes and Hypotenuse](https://mathworld.wolfram.com/RightTriangle.html):** The two sides forming the right angle are called the cathetes or catheti, and the side opposite the right angle is called the hypotenuse. - **[Pythagorean Theorem](https://mathworld.wolfram.com/PythagoreanTheorem.html):** For a right triangle with legs $a$, $b$ and hypotenuse $c$: $$a^2 + b^2 = c^2$$ + +```@raw html +
+ + + + + + + + + + + + + + + + + + + a + b + c + + + a² + b² + c² + + + a² + b² = c² + +
+``` + - **[Pythagorean Triples](https://mathworld.wolfram.com/PythagoreanTriple.html):** a triple of positive integers a, b, and c such that a right triangle exists with legs $a$,$b$ and hypotenuse $c$. This is equivalent to finding positive integers $a$,$b$ and $c$ satisfying the Pythagorean Theorem: - **Examples:** - 1: $(3, 4, 5)$ From 83af59a5f8499b38be06d20c3593b6c80b7ba8cb Mon Sep 17 00:00:00 2001 From: Aron T Date: Sun, 26 Oct 2025 18:00:42 +0200 Subject: [PATCH 5/5] Add SVG diagram for special right triangles (45-45-90 and 30-60-90) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Two triangles side-by-side showing the special right triangle ratios - 45-45-90 triangle: Shows 1:1:√2 ratio with equal legs - 30-60-90 triangle: Shows 1:√3:2 ratio - Clear side labels (a, a√3, 2a) for both triangles - Right angle indicators for both triangles - Centered diagram with titles and ratio information - Angle arc indicators commented out (too difficult to position accurately) Completes all 7 planned diagrams for the Triangles documentation. --- docs/src/Geometry/01 Triangles.md | 61 +++++++++++++++++++++++++++++++ 1 file changed, 61 insertions(+) diff --git a/docs/src/Geometry/01 Triangles.md b/docs/src/Geometry/01 Triangles.md index 7971407..26e087d 100644 --- a/docs/src/Geometry/01 Triangles.md +++ b/docs/src/Geometry/01 Triangles.md @@ -517,6 +517,67 @@ Right triangles have special properties and are fundamental to trigonometry. ### Special Right Triangles +```@raw html +
+ + + + + + + + + + + + + + + + a + a + a√2 + + + 45° + 45° + + + + 45°-45°-90° Triangle + Ratio: 1 : 1 : √2 + + + + + + + + + + + + + + + + + a√3 + a + 2a + + + 60° + 30° + + + + 30°-60°-90° Triangle + Ratio: 1 : √3 : 2 + +
+``` + #### [Isosceles Right Triangle](https://mathworld.wolfram.com/IsoscelesRightTriangle.html) - Angles are 45°-45°-90°