# Questions tagged [euclidean-geometry]

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.

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### Equal products of triangle areas

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### Is it a new discovery on conic section?

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### Generalizing Bottema's theorem

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### Cramer–Castillon problem like

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### Equal sums of line segments

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### Analytic lower-bound for minimal value of $\|x\|^2$ such that $\|Cx-b\|^2 \le c^2$ (a hyperellipsoid)

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### Covering the sphere with an approximately planar grid

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### Generalization of the half-angle formulas

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### Which knots appear as the singular locus of a polyhedral metric on the 3-sphere?

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### Necessary and sufficient condition for quadrilateral to be cyclic

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### Three circles intersecting at one point

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### Collinearity of three significant points of bicentric pentagon

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### Most natural definition of Euclidean geometry [closed]

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### Can the fugitive escape?

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### Is Tarskian hyperbolic geometry consistent, complete & decidable?

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### The set of boundary vectors of compact convex body has empty interior

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### Collinearity in bicentric polygons

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### Looking for journal (without fees) to publish a research paper in Euclidean geometry

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### Necessary and sufficient condition for tangential polygon to be cyclic

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### Embedding an icosahedron

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### Is there an area-preserving concentric diffeomorphism of the ellipse?

**4**

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### Point of concurrency [closed]

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### Smallest regular $m$-gon covering a regular $n$-gon

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### Existence of optimal non-trivial point sets in Euclidean space w.r.t. circumscribed circles of triangles

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### Sufficient coordinate-free condition for points being co-spheric

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### A generalization of Harcourt's theorem

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### Does this plane geometry theorem have a name (well-known)?

**1**

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### A formula for the area of bicentric quadrilateral

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### The centroid, the first and second Napoleon points and $X(930)$ lie on a circle

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### Differential of the gradient of a strictly convex function

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### Four concyclic triangle centers

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### Status of Larry Guth's Sponge Problem

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### Are there any neusis-hard/neusis-complete problems?

**4**

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### Finding Pythagorean quadruples on a given plane?

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### A generalization of Napoleon's theorem

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### Six concyclic points

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### Four concyclic points inside bicentric quadrilateral

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### Intersection point of three circles

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### What are the expected values of the volumes of two classes of ellipsoids contained within the unit 3-ball, and/or what is their ratio?

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### Expected triangle area of normal distributed vertices with colinear expectations

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### What is the expected value of the volume of a tetrahedron inscribed in the unit sphere?

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### How to tile a plane such that moving from one tile to the next in any of the 8 cardinal directions is the same length?

**2**

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### Minimum Euclidean squared norm in the convex hull of points with rational coordinates

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### Lines through the origin every pair of which meet at the same angle

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### Maximizing the volume of the intersection of a fixed ball with a cube with varying width and location

**70**

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### Does this property characterize straight lines in the plane?

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### Can an exterrior of a ball in Euclidean space be considered a ball itself under any proposed generalization?

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### Which subsets of the plane are similar to all their affine images?

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### Solid angles at points in an orthosimplex

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