Questions tagged [synthetic-geometry]
Questions on using GeometricScene, GeometricAssertion, RandomInstance, and FindGeometricConjectures.
16
questions
1
vote
2
answers
72
views
In a triangle ABC with medians $AE$, $BF$, $CD$, we have $\overrightarrow{AE}+\overrightarrow{BF}+\overrightarrow{CD}=0$ with Synthetic Geometry?
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}+\...
- 5,121
5
votes
3
answers
178
views
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 ...
- 345
0
votes
0
answers
173
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 $\...
- 24.3k
4
votes
3
answers
278
views
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 ...
- 24.3k
16
votes
4
answers
624
views
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:
...
- 26.3k
1
vote
0
answers
69
views
RandomInstance of GeometricScene producing unexpected result
Consider the following scene as an example:
...
- 9,113
2
votes
0
answers
58
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 ...
- 51
2
votes
0
answers
65
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),...
- 51
3
votes
2
answers
118
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 ...
- 9,113
1
vote
1
answer
159
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
3
votes
1
answer
113
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
2
votes
1
answer
110
views
How to deduce circle theorems in Wolfram language?
I can deduce the first one by applying FindGeometricConjectures on the following scene:
...
- 9,113
12
votes
1
answer
286
views
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
2
votes
0
answers
91
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 ...
user69323
4
votes
3
answers
331
views
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 ...
7
votes
2
answers
190
views
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