Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with euclidean-geometry
Search options not deleted
user 13093
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.
4
votes
ten concurrent lines
It is possible to give a syhtnetic proof using the following result:
The perpendiculars dropped from the midpoints of a cyclic quadrilateral to the opposite sides are concurrent. Furthermore, thei …
- 2,222
4
votes
Minimum distance between two arbitrary circles in space?
I didn't manage to solve the problem (edit: in the meantime an answer was posted which says a precise formula using radicals cannot be found), but I can post a proof that the line joining the points w …
- 2,222
4
votes
3
answers
3k
views
How to solve geometry problems using involutions
Some geometry problems ( like this and this ) have short solutions if we use involutions. What references are there for solving geometry problems using involutions? I am particularly interested in the …
- 2,222
1
vote
Strengthened version of Isoperimetric inequality with n-polygon
The keyword you are looking for is "quantitative isoperimetric inequalities". The case of polygons was solved in the following paper: https://arxiv.org/abs/1402.4460
The "quantitative" term in the pap …
- 2,222
1
vote
Intersection point of three circles
Switching the roles of $ABC$ and $A'B'C'$, consider the circles passing through the vertices of a triangle $A,B,C$, midpoints of the opposite sides $A',B',C'$ and the circumcenter $O$.
It is straightf …
- 2,222
0
votes
A generalization of Napoleon's theorem
Notice that triangles $ACD, AEB, FCB$ are similar. Working out the ratios of the sides and the angles one can see that:
Triangles $AI_1I_3$ and $ACE$ are similar. Rotating $I_1I_3$ around $A$ with an …
- 2,222
0
votes
Three circles intersecting at one point
It is straightforward to see that $A',B',C'$ are reflections of the circumcenter $O$ with respect to $BC, CA,AB$. Therefore, the center of $(AOA')$ is just the intersection of the mediatrix of $OA$ wi …
- 2,222