All Questions
Tagged with plane-geometry terminology
13 questions
2
votes
1
answer
141
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Does this result above six points follow have a name?
Does this result above six points follow have a name?
Let $A$, $B$, $C$, $D$, $E$, $F$ be six points in the plane and $AB, CF, ED$ are concurrent and $BC, DA, FE$ are concurrent then $CD, EB, AF$ ...
- 1,776
2
votes
2
answers
242
views
A necessary and sufficient condition for three diagonals of a hexagon to be concurrent
When talking about the condition for the three diagonals of a hexagon to be concurrent, we will think of Brianchon's theorem. Using software, I discovered a necessary and sufficient trigonometric ...
- 1,776
5
votes
1
answer
1k
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Is this a new result about hexagon?
Let a hexagon $AB'CA'BC'$ let $AB' \cap A'B=C''$, $BC' \cap B'C = A''$, $CA' \cap C'A = B''$ then three conditions as follows equivalent:
Three lines $AA', BB', CC'$ are concurrent (let the point of ...
- 1,776
2
votes
0
answers
114
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Another Butterfly theorem — Conway like circle
Have You seen these result as follows before?
In Figure 1: $AA'=BB'=tAB$; $CC'=DD'=tCD$, where t is real number then $ABCD$ is a cyclic quadrilateral iff $A'B'C'D'$ is a cyclic quadrilateral.
In the ...
- 1,776
1
vote
0
answers
184
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Writing the plane as {(x,y,z): x+y+z=0} [closed]
One can coordinatize the plane by choosing three axes at 120 degree angles and representing points by triples $(x,y,z)$ with $x+y+z=0$. Is there an accepted name for this kind of coordinate system? (...
- 19.7k
2
votes
1
answer
182
views
Is a line associated with antipodal points (the fact, it is the generalization of Simson line) known?
First time, I found a line associated with antipodal points, detail:
Let $ABC$ be a triangle, $(C)$ is circumconic of $ABC$. $P$ and $P'$ are two antipodal points. Construct three lines through $P'$ ...
- 1,776
5
votes
1
answer
433
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Golden ratio as a property of conic section (is it known?)
I am looking for a proof of a discovery as follows:
Let $ABC$ be arbitrary triangle and $(\Omega)$ be an arbitrary circumconic of $ABC$ let $A'B'C'$ is its tangential triangle of $ABC$ respect to $(\...
- 1,776
1
vote
1
answer
352
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Thirteen-point conic and four-point line, are they new?
We know that Five points determine a conic and Two Points Determine a Line. Here I found a simple construct of a conic through $7$ points (in PS I note that how the conic through thirteen points) and ...
- 1,776
6
votes
0
answers
320
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Does this plane geometry theorem have a name (well-known)?
Consider three circles $(O_1)$, $(O_2)$, $(O_3)$. Denote the homothetic center of $\{$$(O_1)$, $(O_2)$$\}$ by $A$, the homothetic center of $\{$$(O_2)$, $(O_3)$$\}$ by $B$. Let $C$, $D$ be two points ...
- 1,776
3
votes
2
answers
2k
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What is the name of the 65537-gon? [closed]
I know the name of the heptadecagon (17 sides) and the diacosipentacontaheptagon (257 sides). But what is the name of the polygon with 65537 sides? I am unable to figure it.
- 18.7k
60
votes
2
answers
4k
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Does this geometry theorem have a name?
Start with a circle and draw two tangent circles inside. The (black) inner tangent lines to the smaller circles intersect the large circle. The (red) lines through these intersection points are ...
- 509
3
votes
4
answers
513
views
Terminology for polygons
As you may know term "polygon" might mean few different things
and its meaning has to guessed from context.
By some reason I have to use few of these meaning in one place.
So I converge to the ...
- 45k
32
votes
2
answers
1k
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Term for "uncheckable constructions"
Is there a term for "uncheckable geometric constructions"?
Say, Angle Trisection and Doubling the Cube are checkable;
i.e., if the answer is given one can do finite Compass-and-straightedge ...
- 45k