11562
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Constructing a Regular Heptagon Using Lill's Method
This Demonstration shows how to construct a regular heptagon using Lill's method for solving cubic equations.
The points of a regular heptagon with vertices on a circle of radius 1 are given by
. Since
is a solution, if we divide the polynomial
by
, we get
.
If
, then
.
Substituting
leads to the cubic equation
.
It has solutions
,
,
.
This follows from the trigonometric identity
.
Set
and
to get
,
which factors as
.
There are solutions when the points
and
coincide.
Contributed by:
Izidor Hafner
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
Reference
[1] G. E. Martin,
Geometric Constructions
, New York: Springer, 1998 p. 45.
RELATED LINKS
Heptagon
(
Wolfram
MathWorld
)
Theobald's Heptagon-to-Square Dissection
(
Wolfram Demonstrations Project
)
Mechanism for Constructing Regular Polygons
(
Wolfram Demonstrations Project
)
Lill's Method for Calculating the Value of a Cubic Polynomial
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Constructing a Regular Heptagon Using Lill's Method
"
http://demonstrations.wolfram.com/ConstructingARegularHeptagonUsingLillsMethod/
Wolfram Demonstrations Project
Published: September 8, 2017
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Constructing a Regular Heptagon Using Plemelj's Method
Izidor Hafner
Constructing a Regular Heptagon Using Gleason's Method
Izidor Hafner
Hinged Dissection of a Regular Heptagon into Eight Smaller Ones
Izidor Hafner
Swing-and-Twist Hinged Dissection of One Regular Heptagon into Seven
Izidor Hafner
Theobald's Heptagon-to-Square Dissection
Izidor Hafner
Theobald's Dissection of a Heptagon to a Triangle
Izidor Hafner
Theobald's Dissection of a Heptagon to a Pentagon
Izidor Hafner
Dissection of a Regular Dodecagon into Three
Izidor Hafner
Mechanism for Constructing Regular Polygons
Izidor Hafner
Pythagorean Theorem for Regular Polygons
Izidor Hafner
Related Topics
Plane Geometry
Polygons
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+