Intereting Posts

Completion of a Noetherian ring R at the ideal $ (a_1,\ldots,a_n)$
How to show $\zeta (1+\frac{1}{n})\sim n$
The set of irrational numbers is not a $F_{\sigma}$ set.
How to find asymptotics?
Deduction Theorem + Modus Ponens + What = Implicational Propositional Calculus?
For finite abelian groups, show that $G \times G \cong H \times H$ implies $G \cong H$
Show that open segment $(a,b)$, close segment $$ have the same cardinality as $\mathbb{R}$
What is the physical meaning of fractional calculus?
A question concerning a set connected to a sequence of measurable functions
How to prove(or disprove) $\begin{vmatrix} A&B\\ B&A \end{vmatrix}=|A^2-B^2|$
How to solve this trig integral?
Can any smooth planar curve which is closed, be a base for a 3 dimensional cone?
Why is $n_1 \sqrt{2} +n_2 \sqrt{3} + n_3 \sqrt{5} + n_4 \sqrt{7} $ never zero?
Commutative integral domain with d.c.c. is a field
Show that every group $G$ of order $175$ is abelian and list all isomorphism types of these groups

In standard Euclidean geometry, are all equiangular polygons with an odd number of sides also equilateral?

It is easy to prove that all equiangular triangles are also equilateral using basic trogonometric rules.

On the other hand, it is easy to conceive of an equiangular quadrilateral that is not equilateral, i.e. a rectangle.

- combinatorial geometry: covering a square
- Difference between a Gradient and Tangent
- Calculating the height of a circular segment at all points provided only chord and arc lengths
- How many circles are needed to cover a rectangle?
- Is it possible to create a volumetric object which has a circle, a square and an equilateral triangle as orthogonal profiles?
- Why is the volume of a cone one third of the volume of a cylinder?

Extending this further, I can easily conceive of an equiangular hexagon that is not equilateral, but I haven’t been able to visualize an equiangular pentagon that is also equilateral:

Is this true that all equiangular polygons with an odd number of sides also equilateral? If so, is there a straightforward way to prove it? If not, is there a counterexample, an equiangular polygon with an odd number of sides that is not equilateral?

- What does area represent?
- Why do disks on planes grow more quickly with radius than disks on spheres?
- How to parameterize an orange peel
- $7$ points inside a circle at equal distances
- number of primitive Pythagorean triangles whose hypotenuses do not exceed n?
- No hypersurface with odd Euler characteristic
- Find the Closest and Farthest Points of a Cube
- Largest Equilateral Triangle in a Polygon
- Helix with a helix as its axis
- Why ternary diagrams work

No they’re not. Just take your regular pentagon, and pull its base down while preserving the angles. It will get shorter as its adjacent edges get longer.

No. If you take your regular pentagon, for example, you can slide one of the sides away from the center without changing its direction, and extend its two neighbor sides appropriately. This makes the chosen side shorter, two other sides longer, but leaves the angles intact.

- Fourier transform as a Gelfand transform
- Sum identity using Stirling numbers of the second kind
- Prove that for any element $b$, $|b|$ divides $|a|$ (order of $b$ divides order of $a$).
- Help proving that a Banach space is reflexive
- Surprising but simple group theory result on conjugacy classes
- How to write a good mathematical paper?
- A nonnegative random variable has zero expectation if and only if it is zero almost surely
- Can there be a set of numbers, which have properties like those of quaternions, but of dimension 3?
- A question regarding Markov Chains
- All Sylow $p$-subgroups of $GL_2(\mathbb F_p)$?
- Prove the following equality: $\int_{0}^{\pi} e^{4\cos(t)}\cos(4\sin(t))\;\mathrm{d}t = \pi$
- Which “limit of ultrafilter” functions induce a compact Hausdorff topological structure?
- How to Compare two multiplications without multiplying?
- $M_3$ is a simple lattice
- Greatest prime factor of $n$ is less than square root of $n$, proof