From Kenneth: I was wondering, is there a relationship between the number of sides of a regular n-gon and the number of times its diagonals intersect?
4 sides=1 intersect (center, diagonals form an 'X' )
5 sides=5 intersects (diagonals form a star)
6 sides=13 intersects
And so on. Answered by Chris Fisher.
From Sandra: One of my son's math questions is as follows:
Suppose I have a shape with 10 sides. I choose a vertex then draw lines to the other vertices that dont share sides with the first vertex. How many vertices will that be and why? Answered by Penny Nom.
From jenea: I have to find the perimeter as well as the area of a rectangle when given the diagonals are 12 units long and they intersect at a 60 degree angle. how do i find both the area and perimeter; do i use the 30 60 90 triangle rule? Answered by Stephen La Rocque and Penny Nom.
From John: I have a cylinder that is 37.5" width X 25.25" circumference. I need to create a repeating diagonal lined pattern on the cylinder so that when it prints it joins perfectly at the circumference repeat. The design must follow these specs.
Black diagonal lines need to be 1.250" max width X 1.5" max spacing between the black lines.
Please Help Answered by Stephen La Rocque.
From matthew: in a rectangular grid 3600x288 (or any large rectangle with an even number of units) how can I determine the number of vertices a diagonal line will pass through? Answered by Stephen La Rocque and Penny Nom.
From Joshua: A dodecahedron has twelve faces, all of which are regular pentagons. Three edges meet at each vertex of the dodecahedron. An interior diagonal is a segment connecting two vertices such that the segment is not an edge or along a face of the dodecagedron. How many interior diagonals does a regular dodecahedron have? Answered by Penny Nom.
From Murray: If you have a regular polygon with n sides and you draw all (n-3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into. Answered by Caude Tardif and Chris Fisher.
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.