Questions tagged [synthetic-geometry]

Questions on using GeometricScene, GeometricAssertion, RandomInstance, and FindGeometricConjectures.

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How to plot Morley triangle by Synthetic Geometry method?

As the Wiki The three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle So I write this code: ...
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Intersection of 3 circles in GeometricScene

I am trying to represent the image below in Mathematica and can't seem to make it work. There doesn't seem to be any constraint of type circle intersection in the documentation. I tried this: ...
• 123
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Symbolic formula from GeometricScene?

I'm trying to solve the following problem with GeometricScene What is the shortest circular arc of which the altitude above its chord is one? I have the following code: ...
• 408
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Parellel-To-Plane Version of RegionDistance

RegionDistance basically calculates distance between points P and Q=RegionNearest[Reg,P]: I need to find a way to find function ...
• 407
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How to construct the Nagel point of a triangle with GeometricScene?

Let us consider the Nagel point of a triangle. According to this article,"There exists an easy construction of the Nagel point. Starting from each vertex of a triangle, it suffices to carry twice ...
• 27.4k
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How to calculate the degree of $∠FEB$ under this geometric scene

I want to calculate the $∠FEB$ in the figure below, but I can't solve this question with GeometricScene function. What can I do to find the answers to these ...
131 views

I am trying to set up Mathematica Synthetic Geometry stuff to prove the following: Given a triangle ABC with medians $AE$, $BF$, $CD$. Show that we have $\overrightarrow{AE}+\overrightarrow{BF}+\... • 5,441 3 votes 2 answers 223 views How to solve a geometric problem about a triangle using GeometricSolveValues? I try to solve not so difficult geometric problem from an exercise book on elementary math with 14.0 on Windows 10: Let a triangle$\triangle ABC$be given and the area of$\triangle ABC$be equal to ... • 27.4k 3 votes 2 answers 122 views Can I make RandomInstance use exact arithmetic? When using RandomInstance on a GeometricScene the answer loses precision when root objects are encountered. Is there a way to ... • 9,543 3 votes 1 answer 116 views How to define the intersection of two lines as a point I tried the code below (I sort of translated it from written notation), where I hoped that [Intersection] would give me the intersection of line ac with the altitude from b: ... • 197 3 votes 0 answers 67 views GeometricScene extremely slow or cannot complete I would like to find instances of the following dodecahedral wheel generalized to the situation where the red squares become rhombuses. I tried this using RandomInstance[GeometricScene], but ... • 61 2 votes 1 answer 114 views How to deduce circle theorems in Wolfram language? I can deduce the first one by applying FindGeometricConjectures on the following scene: ... • 9,543 2 votes 0 answers 70 views GeometricScene is slow and does not find an answer to a visually obvious problem for many points I'm trying to use GeometricScene to visualize a finite patch of a periodic tiling of triangles and rhombi. When I require the rhombi to be squares (using "Regular" property on the Polygons),... • 61 2 votes 0 answers 96 views How can I calculate the ratio of the line segments in the following geometric scene? The following code can draw the corresponding geometric scene. By observing for many times, we can know that the length ratio of line CE and line ... 1 vote 1 answer 165 views Locating the intersections of two circles in a GeometricScene where the points are symbolic I'm trying to intersect two circles in a GeometricScene. ... • 343 1 vote 2 answers 93 views Including all constraints in a geometry problem I'm trying to solve this geometry problem using GeometricScene: Find angle x: Here's my (incomplete) code: ... • 41.9k 1 vote 0 answers 76 views RandomInstance of GeometricScene producing unexpected result Consider the following scene as an example: ... • 9,543 0 votes 0 answers 178 views The Nagel point revisited Let$i$be the incenter of the triangle$\triangle abc$, and$n$be the Nagel point of this triangle (see Wiki ). Let also$h_3$and$h_2$be the orthocenters of the triangles$\triangle iab$and$\...
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I try to solve the following problem, making use of 14.0 on Windows 10 Let a triangle $\Delta$ (a contour with its interior) be chosen in the unit square $S$. To prove that the closure of the ...