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Results tagged with euclidean-geometry
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user 122662
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.
2
votes
Dao's theorem on six circumcenters associated with a cyclic hexagon
The solution of problem in our paper On an Extension of Miquel's Theorem to a Cyclic Hexagon;
Relative configuration in here On the eight circles theorem and its dual
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-1
votes
2
answers
318
views
A Erdős–Mordell Like inequality
Ono's inequality is true for acute triangle but false with general triangles. The inequality as follows is false with general triangls but I think it true with acute triangle (follows answer by Fedor …
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3
votes
0
answers
298
views
A problem on configuration of Dao's theorem on six circumcenters
Abstract: In the figure belows: Three lines through center of pair opposite red circle are concurrent. This is a statement of Dao's theorem on six circumcenter, a new theorem in plane geometry which w …
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2
votes
0
answers
211
views
A generalization of the Archimedean circle
I proposed a generalization of the Archimedean circle : In this figure $M$ is the midpoint of $AB$, $DE$; $(G)$, $(H)$, $(M)$ are the semicircles. Then two yellow circles are congruent.
Question: Is t …
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1
vote
0
answers
111
views
Is the formula known? and can we generalized for higher dimensions?
In this configuration as follows, we have a nice formula:
$$\cos(\varphi)=\frac{OF.OE+OB.OC}{OF.OB+OE.OC}$$
Is the formula known? and can we generalized for higher dimensions?
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3
votes
1
answer
403
views
Generalization of Tucker circle, Conway circle and van Lamoen circle
Theorem 9.1 in this paper as follows is a generalization of Turker circle. Turker circles is a generalization of many circles as: Cosine Circle, circum circle, First Lemoine Circle, Gallatly Circle, K …
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1
vote
An new equilateral triangle related to the Morley triangle
Today I have just been found that the theorem above was found early by Dr. Floor van Lamoen. His paper Equilateral chordal triangles.
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11
votes
Does this geometry theorem have a name?
This is theorem 2 (the Parallel tangent theorem) in "Two Applications of the Generalized Ptolemy Theorem" by Shay Gueron.
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3
votes
1
answer
173
views
Relative to Isoperimetric inequality with n-polygon
Since Brahmagupta's formula and Bretschneider's formula we have the inequality:
Any two quardrilaterals $A_1A_2A_3A_4$ and $B_1B_2B_3B_4$ with the same sidelengths and $A_1A_2A_3A_4$ is a cyclic b …
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2
votes
1
answer
371
views
Yiu's equilateral triangle-triplet points
In more than 2300 years since Euclid's Elements appear, there were only two equilateral triangles become famous: The Morely equilateral triangle and the Napoleon equilateral triangle. In more than 200 …
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2
votes
0
answers
166
views
Pascal theorem for three dimensions
A year ago I found the Pascal theorem for three dimentions as follows:
Let $(C_1)$, $(C_2)$ be two conics on the same Ellipsoid, (or Hyperboloid, or Paraboloid). Let $A_1$, $A_2$, $A_3$, $A_4$, $A_5$ …
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5
votes
0
answers
341
views
$N$-$th$ closed chain of six circles
Since 2013, I found a very nice configuration: $N$-th closed chain of six circles. This is a generalization of theorem 1, problem 2 in here and theorem 2 in here and here (and is also generalizatio …
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3
votes
0
answers
886
views
A generalization of the Sawayama-Thebault theorem
1. Introduction
The Sawayama-Thebault theorem is one of the best nice theorem in plane geometry. The theorem has a long history. It was published in AMM in 1938 the first solution appeared in 1973 wi …
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3
votes
0
answers
231
views
Are these points known? [closed]
Let $ABC$ be a triangle and $P$ be a point on the plane, $PA$, $PB$, $PC$ meet $BC$, $CA$, $AB$ at $A'$, $B'$, $C'$ respectively.
From my construction by GeoGebra, I found two special points as follow …
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3
votes
1
answer
503
views
An new equilateral triangle related to the Morley triangle
Morley equilateral triangle is the nice theorem in Eulidean Geometry. I found an equilateral triangle and a group circle related to the Morley triangle and angle trisectors:
Let $ABC$ be a triangle …
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