polygons

  1. L

    Limit of inscribed regular polygons

    An equilateral triangle of side 1 is inscribed by the largest square possible which is inscribed by the largest regular pentagon possible, ad infinitum. What is the radius of the limiting circle?
  2. R

    Geometry Similar Polygons

    I need help with solving these questions. I’m having trouble with setting up the proportion and finding the scale factor. For #2a, would the proportion be 10/15 and 15/20?
  3. 7

    [Help] The number of possible k-sided polygons in an m by n grid of dots

    Hello. :spin: This is my first post, so sorry for the potential mistakes below. A grid of dots has the dimensions m by n, where m is greater than or equal to n. Pick k dots from this grid in such a way that they form a polygon with k sides. In other words, no three dots can be collinear...
  4. S

    When were constructible polygons actually constructed?

    Gauss proved in 1796 that 17-gon could be constructed - but did not actually show how to do so. The first construction of heptadecagon was by Erchinger, several years later - and it does not appear to be the best, because several constructions are offered with later dates. In 1801, Gauss showed...
  5. T

    Polygons in a cube

    Hello, the situation is the following: A cube is intersected by a plane. Depending on the coordinates of the plane, different polygons can be created by the intersection. How can I prove (with analytic geometry) that these polygons can be triangles, rectangles, pentagons or hexagons...
  6. M

    Sticks and polygons

    Hi there, I have 5 sticks of the same length. All the sticks have to be linked. How many distinct polygons can I build? We assume that 2 polygons are identical if they have the same area it does not matter how they are oriented in 2D plan. Thank you
  7. C

    geometry - polyhedra and polygons

    triangle POY is one of four triangular faces in the polyhedron - name the other 3 faces ? The line segment where two faces meet is called an edge. Line segment PO is one of 6 edges in the polyhedron. Name the other 5 ? A point of intersection of 3 or more edges is called a vertex of...
  8. M

    star polygons

    Does anyone know of a good book on star polygons? And if anyone knows of good online resources forr learning more about them, please either reply with a link or send me a private message with one if you can't post a link here.
  9. M

    polygons

    Convex polygons has 3 Internal obtuse angle How many sides polygon
  10. C

    polygons

    Audra drew two rectangles on a coordinate plane. The first rectangle has vertices at (-6, 3), (-6, 6), (-4, 3), and (-4, 6). The second rectangle has vertices at (-4, 2), (-4, 4),(-2 2/3, 2) , (-2 2/3, 4). Why are these two rectangles similar? A. The area of the new rectangle is...
  11. C

    polygons

    Audra drew two rectangles on a coordinate plane. The first rectangle has vertices at (-6, 3), (-6, 6), (-4, 3), and (-4, 6). The second rectangle has vertices at (-4, 2), (-4, 4),(-2 2/3, 2) , (-2 2/3, 4). Why are these two rectangles similar? A. The area of the new rectangle is...
  12. D

    Bounding General Shapes with Polygons, Especially Concave

    I created an unproven algorithm (or heuristic) back in 1999/2000 for bounding shapes with polygons. It was interesting because it was fast, general for polygons of any number of sides, and especially that it worked for concave polygons. Is this a solution out in the wild? Did someone else...
  13. S

    faces of two polygons and lines intersections

    Hi everyone, If a polygon is inside a rectangle, and a set of vertical parallel lines where each of them pass through one vertex creating new faces. Is there a way to determining the points of the new faces, when a vertical parallel lines cut polygon that lies inside rectangle?
  14. B

    Tiling by Nested Polygons

    Nested polygons generate logarithmic spiral curves and are good examples of contraction mappings. We can use nested polygons to tile the plane and get beautiful tessellations: These pictures are very easy to make using GeoGebra. More tessellations and a few GeoGebra examples are here.
  15. A

    Area Changes in Irregular Polygons

    Hi All, I have a question regarding calculating the area of irregular polygons using two pieces of information. I'll give you some background - I work in a seat company where we are looking to reduce the seam allowance on material patterns that we use to make seats. We have many different...
  16. P

    Polygons can be designated as N-gons.What about of vertices?

    Hi In 3D modeling world, people refer to 3 sided polygons as tris, 4 sided as quads and >4 sides polygons as N-gons. Now, if I understand right, actually N-Gon refers to any. So instead of saying Triangle or Quadrilateral, I can say 4-gon and it would be correct right? What about vertices...
  17. B

    Rolling Regular Polygons around a Circle

    Rolling Regular Polygons around a Circle
  18. B

    Superposing Star Polygons

    Hello everyone! :D Regular Star Polygon {n/k}: Formulas and Examples :D Superposing Star Polygons (1): n = 32, k = 1 ~ 15 :D Superposing Star Polygons (2): n = 3 ~ 40 Thank you for watching and best regards.
  19. P

    Equilateral Curve Heptagon- Construct Similar Polygons ?

    Similar to Equilateral Curve Heptagon(polygon of 7 sides), Can we can also construct the polygon (diameter remains constant) applicable to polygon of n sides ? http://www.mathopenref.com/heptagon.html i.e For example Equilateral Curve Pentagon(polygon n=5 sides) Equilateral Curve Hexagon...
  20. M

    dividing polygons into rhombuses

    I'm trying to prove that any regular and convex 2n-polygon can be divided into rhombuses. I proceed by induction. BASE CASE: For n=2 this is obviously true because a square is a rhombus. INDUCTIVE HYPOTHESIS: suppose the statement is true for a polygon with 2n sides. Now to make a polygon with...