Homework Answers
We need to assume the vertices are in "general position."
Take any 4 vertices. One pair of chords determined by these vertices meets inside the polygon, the other two do not. So the number of chord intersections inside the polygon is (nC4).
So, 
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A regular n-gon is a polygon with n sides of equal length, in which all angles...
A regular polygon is an n-sided polygon in which all sides are of the same length...
A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon isArea =Here, s is the length of a side. Write a program that prompts the user to enter the number of sides and their length of a regular polygon and displays its area. Here is a sample run:
//include comments Opts (Regular polygon) An n-sided regular polygon has n sides of the same length...
//include comments
Opts (Regular polygon) An n-sided regular polygon has n sides of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). Design a class named RegularPolygon that contains: Aprivate int data field named n that defines the number of sides in the polygon with default value 3. A private double data field named side that stores the length of the side with default value 1. A private double data field...
(Geometry: n-sided regular polygon) An n-sided regular polygon’s sides all have the same length and all...
(Geometry: n-sided regular polygon) An n-sided regular polygon’s sides all have the same length and all of its angles have the same degree (i.e., the polygon is both equilateral and equiangular). Design a class named RegularPolygon that contains: ■ A private int data field named n that defines the number of sides in the polygon. ■ A private float data field named side that stores the length of the side. ■ A private float data field named x that defines...
N-Sided Polygon An n-sided polygon is a planed figure whose sides have the same length and...
N-Sided Polygon An n-sided polygon is a planed figure whose sides have the same length and whose angles have the same degree. Write a class called NSidedPolygon that contains the following components: Private members to store the name of a polygon, the number of sides, and the length of each side. (You are expected to select the appropriate data types for each member.) A constructor that accepts the number of sides and the length of each side. A private method...
Write a program that displays a convex regular polygon with m or n sides, where m...
Write a program that displays a convex regular polygon with m or n sides, where m is the last digit of your student number plus 3, n is the second last digit plus 3. Use two buttons named “before” and “after” to change the number of sides of the polygon. Click on “before” button will show a convex regular polygon with m sides and click on “after” will show a convex regular polygon with n sides. For example, a student...
Problem 2 9.9 Geometry: n-sided regular polygon pg. 362 (25 points) Follow instructions as provided on...
Problem 2 9.9 Geometry: n-sided regular polygon pg. 362 (25 points) Follow instructions as provided on page 362, reprinted below 9.9 (Geometry: n-sided regular polygon) In an n-sided regular polygon, all sides have the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular) Design a class named RegularPolygon that contains A private int data field named n that defines the number of sides in the polygon with default value of 3 A...
Write a simple class representing a Polygon up to 6 sides: the Polygon class has 5...
Write a simple class representing a Polygon up to 6 sides: the Polygon class has 5 fields: Regular, sides, sideLength, angle, apothem Polygon: Regular: boolean sides: int sideLength: double angle : double apothem : double Provide a no-arg constructor for this class initializes the object and sets the instance variables to: Regular: true sides: 3 sideLength: 1 angle : 60 apothem : SquareRoot(3)/2 Provide the following methods: Set number of sides set the length of the sides set the angle...
3. (6 points) Consider the regular pentagon ABCDE with sides of length 1 and three diagonals...
3. (6 points) Consider the regular pentagon ABCDE with sides of length 1 and three diagonals as shown. Let the diagonals have length. The measure of each interior angle of a regular pentagon is 108° The isosceles triangles ABF and ECD are similar and each have angles 369-36° -1080 (a) Use a proportion for similar triangles ABF and ECD and the quadratic formula, -btVb2-4ac dc to show that x = * (the golden ratio). 2a * 360 x (diagonal) (b)...
1. Let ABCDE be a regular pentagon on the unit sphere S with each side equal to s and each angle equal to 4pi/5. Find the exact value of cos a. Noticed that as in Euclidean geometry a regular pe...
1.
Let ABCDE be a regular pentagon on the unit sphere S with each side
equal to s and each angle equal to 4pi/5. Find the exact value of
cos a. Noticed that as in Euclidean geometry a regular pentagon
called a spear can be inscribed in a spherical circle
The only ideas that can be used include: area ABC-RA2(A+B+C-Ipi), the Pythagorean theorem: Cos c-cos a cos b. Vectors-dot product cross product, sin A-sin a/sin c; coS A-COs a sin...
ANSWER 2 & 3 please. Show work for my understanding and upvote. THANK YOU!! 2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip...
ANSWER 2 & 3 please. Show work for my understanding and
upvote. THANK YOU!!
2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip over the n-gon. These n actions form a group denotecd (a) Draw a Cayley diagram for Cn for n-4, n-5, and n-6 (b) For n 4, 5, 6, find all minimal generating sets of C.· [Note: There are minimal generating sets...
A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon isArea =Here, s is the length of a side. Write a program that prompts the user to enter the number of sides and their length of a regular polygon and displays its area. Here is a sample run:
//include comments
Opts (Regular polygon) An n-sided regular polygon has n sides of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). Design a class named RegularPolygon that contains: Aprivate int data field named n that defines the number of sides in the polygon with default value 3. A private double data field named side that stores the length of the side with default value 1. A private double data field...
Problem 2 9.9 Geometry: n-sided regular polygon pg. 362 (25 points) Follow instructions as provided on page 362, reprinted below 9.9 (Geometry: n-sided regular polygon) In an n-sided regular polygon, all sides have the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular) Design a class named RegularPolygon that contains A private int data field named n that defines the number of sides in the polygon with default value of 3 A...
3. (6 points) Consider the regular pentagon ABCDE with sides of length 1 and three diagonals as shown. Let the diagonals have length. The measure of each interior angle of a regular pentagon is 108° The isosceles triangles ABF and ECD are similar and each have angles 369-36° -1080 (a) Use a proportion for similar triangles ABF and ECD and the quadratic formula, -btVb2-4ac dc to show that x = * (the golden ratio). 2a * 360 x (diagonal) (b)...
1.
Let ABCDE be a regular pentagon on the unit sphere S with each side
equal to s and each angle equal to 4pi/5. Find the exact value of
cos a. Noticed that as in Euclidean geometry a regular pentagon
called a spear can be inscribed in a spherical circle
The only ideas that can be used include: area ABC-RA2(A+B+C-Ipi), the Pythagorean theorem: Cos c-cos a cos b. Vectors-dot product cross product, sin A-sin a/sin c; coS A-COs a sin...
ANSWER 2 & 3 please. Show work for my understanding and
upvote. THANK YOU!!
2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip over the n-gon. These n actions form a group denotecd (a) Draw a Cayley diagram for Cn for n-4, n-5, and n-6 (b) For n 4, 5, 6, find all minimal generating sets of C.· [Note: There are minimal generating sets...
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