# What is Hexagon: Definition and 43 Discussions

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon or 6-gon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

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1. ### I Looking for the spectrum of equilateral drums

Hi Pfs, I found the formulas for the frequencies of half square triangles, and rectangles. But nothing on hexagonal drums or equilateral triangles. (it would nice to get them with Dirichlet and Neumann bordery conditions) thanks
2. ### Particles moving on a regular hexagon

When I first read the question, it didn't occur to me that these particles would ever meet or catch up with their neighbors. They are all traveling from one vertex to another with a velocity ##v## and a distance ##a##, all either clockwise or anticlockwise right ? The question says "Each...
3. ### MHB Can Parallelograms Be Constructed in a Convex Hexagon?

In a convex hexagon $ABCDEF$ exist a point $M$ such that $ABCM$ and $DEFM$ are parallelograms . Prove that exists a point $N$ such that $BCDN$ and $EFAN$ are also parallelograms.
4. ### Point charges in a regular hexagon

The answer should be (2×sqrt3×k×q^2)/a^2. What did I do wrong?
5. ### How to calculate the magnitudes of three forces around a hexagon

Can anyone please help me with the following? Three forces which act along the sides AB, BC and CD of a regular hexagon ABCDEF of side 2a, have a resultant which acts along DF. When a couple of 4Pa in the sense CBA is added in the plane of the hexagon, the resultant acts along CA. Find the...
6. ### Magnetic mirror: pentagon or hexagon toroid?

I know that the problem of magnetic mirrors is that they leak out the tight ends of the mirror, on the other hand the main problem of toroids is that magnetic field line curvature creates a better confinement on the inner diameter and lesser on the outer diameter so needs a strong plasma current...
7. ### 5 charges placed at 5 vertices of a regular hexagon

If 5 charges (each q) are placed at 5 vertex of a regular hexagon of side a then effectively the electric field at the centre of the hexagon is $$\frac{q}{4\pi\epsilon_0a^2}$$ but the potential is $$\frac{5q}{4\pi\epsilon_0a}$$ but then what about $$V=-\int \textbf{E•dr}$$
8. ### MHB Is there a non-regular hexagon

How can I prove that If there the only hexagon that his sides equal one to each other then it angles can't be different one from each other?
9. ### I "Banana clock shapes" puzzle on social media

I looked for an answer to this question other places but found none. There is a puzzle going around that people are getting the answer wrong to. No surprise there. According to the proofs I found for it on the internet, my assumptions were true and I did arrive at the right answer (38...
10. ### Area of Hexagon - Geometry Challenge

Determine the area of the painted hexagon, knowing that the area of triangle ABC is 120cm^2 IMG Link: https://m.imgur.com/a/WtdsW I tried using Heron´s formula, but just ended up with a bunch of terms and one more variable. Sidenote: I guess part of it is figuring out that the side lenghts...
11. ### MHB Calculating Ratio of $\overline{BP}$ to $\overline {PN}$ in Hexagon $ABCDEF$

Regular hexagon $ABCDEF$,points $M$ and $N$ are midpoints of $\overline{CD}$ and $\overline {DE}$ respectively, point $P$ is the intersection of $\overline {AM}$ and $\overline{BN}$ Find $\dfrac {\overline{BP}}{\overline {PN}}$
12. ### MHB Solving Hexagon Question: What Else Do I Need to Know?

I know AM is 10... and that's it. I don't know.
13. ### Hexagon's rotating in a larger hexagon

Hello The attached diagram shows a group of 6 hexagons rotating inside a larger hexagon. I have never seen such rotation before and didn’t envisage it until I drew it. Just out of curiosity I was hoping someone could advise of any documentation on such rotation. I cannot see any substantial...
14. ### Moment of Inertia of a Regular Hexagon

A equilateral triangular lamina, has a moment of Inertia of I if the axis of rotation passes through the centroid of the triangle, perpendicular to it's plane. What is the moment of inertia of a regular hexagon(Again, through it's geometrical centre, perpendicular to the plane), provided that...
15. ### Find matrix representation for rotating/reflecting hexagon

Homework Statement Consider the set of operations in the plane that includes rotations by an angle about the origin and reflections about an axis through the origin. Find a matrix representation in terms of 2x2 matrices of the group of transformations (rotations plus reflections) that leaves...
16. ### Area of hexagon is maximum while perimeter is fixed

this is the given problem: and this is my attempt at a solution: I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so. Thanks for any help!
17. ### MHB Probability problem in hexagon

So say I have 6 bugs standing on the 6 vertices of a hexagon, one per vertex. And say they each pick a vertex that they are not currently on, and starts moving in a straight line towards that vertex at the same speed. So my question is how many possibilities are there for the bugs to move to the...
18. ### Saturn's north pole hexagon vortex ring

New photo released today from NASA showing remarkable detail of a hexagon vortex ring at Saturn's North pole. http://www.space.com/24534-saturn-hexagon-vortex-nasa-cassini-photo.html Anyone see any papers explaining how the ring gets its shape?
19. ### Linear Algebra on a Regular Hexagon

Homework Statement We are supposed to compute the magnitude of vectors that make up a regular hexagon. We are given the magnitude of one side (its magnitude is 1). We are also supposed to compute one of the interior angles. Homework Equations I feel like this isn't enough...
20. ### Solving Hexagon Area: Formula Troubles and Possible Solutions

I've found a formula for the area of a regular hexagon,but it seems to falter when i try to finds its area using the apothem sometimes,i know the formula is not wrong because i derived and verified it's authenticity so that can't be it. I heard that by not utilizing the apothem formula, you...
21. ### MHB Coordinates of Hexagon Vertices in Base (AC, AD)

Consider a regular hexagon ABCDEF (in order counterclockwise). Determine the coordinates of AB, AE AND AF (->) in the base (AC, AD) (->) AB(->)=(_____,_____) AE(->)=(_____,_____) AF(->)=(_____,_____) what I mean with exemple AF(->) positive way from A to F. I have draw a it but I got problem...
22. ### MHB Ilovethepopper's question at Yahoo Answers concerning the width of a hexagon

Here is the question: Here is a link to the question: Math problem, law of cosines.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
23. ### Determining Areas of Triangles in Hexagon ABCDEF

I have hexagon ABCDEF (30 cm2) and point M inside. True: ABM = 3 cm2; BCM = 2 cm2; DEM = 7 cm2 ; FEM = 8cm2 How can I determine area of others two triangles? I know their total area, but how individually? Thanks very much and if you don't understand, write, I will try to write better...
24. ### Calculating equilibrant in regular hexagon

Homework Statement In a regular hexagon, ABCDEF, forces of magnitude 2N, 4N, 3N and 2N act along the lines AB, AC, AD and AF respectively. Find the equilbrant of the given forces and verify that is equal and opposite to their resultant. The Attempt at a Solution I realized that AB + BC...
25. ### Regualr hexagon and position vector - how does this work

Homework Statement a regular hexagon OPQRST has its vertices at O ( the origin) and points P,Q,R, S,T with position vector p,q,r,s,t respectively. The point U with position vector u is the midpoint of the line segment OP, and SU meets OR at the point V please see attached diagem I need...
26. ### How many ways can you color the edges of a hexagon in two colors?

Homework Statement How many ways can you color the edges of a hexagon in two colors? It is assumed two colorings are identical if there is a way to flip or rotate the hexagon. Homework Equations Orbit Stabilizer Lemma and Burnside's LemmaThe Attempt at a Solution This, implements the Orbit...
27. ### MHB Vector of regular hexagon

ABCDEF is a regular hexagon with $\vec {BC}$ represents $\underline {b}$ and $\vec {FC}$ represents 2$\underline {a}$. Express, vector $\vec {AB}$, $\vec {CD}$ and $\vec {EC}$ in terms of $\underline {a}$ and $\underline {b}$. Before I start, I want to ask if we need to redefined \$\underline...
28. ### Finding Effective Resistance Across A Hexagon: A Homework Solution

Homework Statement The diagram represents a regular hexagon. The resistances are r each Find the effective resistance across points A & B http://tinypic.com/r/153n39d/7 Homework Equations The Attempt at a Solution A resistance less wire passes through one of the diagonals...
29. ### Polar Coordinates, Six-Pointed Star, and a Hexagon

Homework Statement Hey I have to create a six-pointed star and a hexagon with polar coordinates using MATLAB. I don't need help with using MATLAB, I just need help with the math. Note that I don't really need to know how the math sense this assignment is for a CSE course. I just don't...
30. ### How do I find the net capacitance across AO?

Homework Statement The Attempt at a Solution There were 4 parts to find net capacitance across AD, FE, AE and AO I need help with AO and i don't have any idea how to do it
31. ### Calculate the electric potential at the center of the hexagon

A plastic rod with a total charge Q uniformly distributed along its length is bent into a regular hexagon where each side has a length of 2a, as shown below. Calculate the electric potential at the center of the hexagon (relative to the point at infinity). I wasn't sure how to exactly start...
32. ### Does Saturn Have a Hexagon on it?

As the title says, just seen this Video... http://www.youtube.com/watch?v=qzL194jiTyY&feature=player_embedded#t=107 Is that real??
33. ### Hexagon Book puzzle that doesnt work

Hi guys, I was given a puzzle book resently (Brain Training Puzzles; Difficult Book 1; Carlton) and rather excited cause I really want to get into logic/maths puzzles. So I have only got a few pages in and saw two grid of hexagons either blue or red and the questions goes: "The colour of each...
34. ### What is the velocity of the opposing rod in a hexagon mechanics problem?

Here's a mechanics problem that seems pretty straightforward, but I can't get anywhere on it. You have a system of six rods arranged in a regular hexagon, connected by hinges at each vertex, giving some non-rigid structure. Now you apply a force to one of the rods in a direction perpendicular...
35. ### Hexagon Shaped Cloud on Saturn

Here's a picture of it http://www.nasa.gov/mission_pages/cassini/multimedia/pia09188.html I found this very striking and am surprised that there has been so little talk about it. My best guess is that it has something to do with tidal forces being exerted by multiple moons. I'm...
36. ### Find a+b in Regular Hexagon Complex Plane Problem

Homework Statement A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let R be the region outside the hexagon, and let S = \{ 1/z |x \in R} . Then the area of S has the form a \pi...
37. ### Find Area of Triangle QLP & XYZ in Hexagon

Homework Statement A right angled triangle has 3 squares attached to each side(the measure of each is givn in the figure). a hexagon is thus formed. Find its area. Homework Equations none The Attempt at a Solution I have found the area of the figure except for the following...
38. ### Area of a Hexagon: Find the Area with Radius r

Homework Statement A circle of radius r is impressed in a hexagon. Find the area of the hexagon. Homework Equations Area of a triangle = (1/2)bh The Attempt at a Solution The hexagon can be split up into six triangles, and with the formula for the area of a triangle, becomes...
39. ### Hexagon on Saturn: NASA Investigates

SATURN What could be the cause of this hexagon feature on saturn http://www.jpl.nasa.gov/images/cassini/pia09188-browse.jpg http://www.nasa.gov/mission_pages/cassini/multimedia/pia09187.html
40. ### Saturn's hexagon and his accretion disk jets

Hi! What do you know about Saturn's Nord Pole hexagon? Is sure than the Saturn's hexagon is owed to nothing else but his convection. Then we ask ourselves what fact makes the convection from the Saturn's North Pole. There are two possibilities: 1). the convection is due to a temperature...
41. ### Sum of interior angles of cyclic hexagon

Right I have been given the following problem and cannot resolve it. I have had an attempt but without much success. Could anyone help me with this exercise, please? Hints or a little more welcome :-) A cyclic hexagon is a hexagon whose vertices all lie on the circumference of a circle...
42. ### Circumscribed and inscribed circles of a regular hexagon?

Hey ppl, Could anyone help me with this: what is the ratio of the areas of the circumscribed and inscribed circles of a regular hexagon? how do I go about working it out from first principles? Cheers, joe
43. ### How Is the Electrical Force Calculated on a Charge at the Center of a Hexagon?

I'm having a little trouble with this one.. Three pointlike charges Q are located on three successive vertices of a reguar hexagon with sides "l". Find the electrical force on another charge q located at the center of the hexagon. Assume all the charges are like charges. ( all positive )...