Welcome to Ian's geometry forum!

    This site tells you all about constructions and how to make them, with a special emphasis on the constructions of polygons.

A new and successful general rule for the approximate construction of regular polygons!

As follows, here is a list of some of the regular polygons that can be constructed approximately or exactly.

Equilateral Triangle Nonogon 15-gon
Square Decagon 16-gon
Pentagon 11-gon 17-gon
Hexagon 12-gon 18-gon
Heptagon 13-gon 19-gon
Octogon 14-gon 20-gon

 

    Please check back later as I will be adding more constructions of polygons with increasing numbers of sides as my site grows.

Here is a list of other constructions:

 

Construct a Parallel Divide a line segment by n 1
Construct a Parallel with Straightedge (Ceva's Theorem) Divide a line segment by n 2
Construct a Fourth Segment in Proportion to Three Divide a line segment by n 3
Constructing a Tangent Trisect a 90° angle
Construct a Tangent From a Point Kochansky Pi
Construct a line segment in the golden ratio Square Root of a Segment
Trisect the Area of a Triangle Square Root of a Segment 2
Construct the perpendicular bisector of a segment Construct Geometric Mean
Bisect a line segment Construct Perpendicular to a Line
Bisect a Line Segment With a Compass Bisect an Angle
Constructing a Triangle with Sides of Given Length Trisect a line segment

 

Some constructions show things. Here are some of them. (These pages tend to be short. For a comprehensive list of them, click here).

 

Nine Point Circle Parallel Triangle Area
Altitudes of any Triangle Monge's Circles Theorem
Medians of any Triangle The Pythagorean Theorem
Perpendicular Bisectors of the Sides of any Triangle Triangles
Angle Bisectors of any Triangle SAS Triangle Area
Inscribed Angles in a Circle Euler's Line
Ian's Theorem  

Click here to go to the Calculations Page

    In the couse of history, many constructions were published that were incorrect. As follows, here are two of them. Many of those published were "solutions" to "Problems of Antiquity". Since they were discovered, people have tried to solve them. Only recently (about 200-300) years ago were they all proved to be impossible. Click here to go to my Problems of Antiquity page.

 

Trisect an Arbitrary Angle

Pentagon

 

To view a special page for people with Geometer's Sketchpad, click here. Get Geometer's Sketchpad.

Click here to go to my Downloads Page.

For my bibliography, click here.

Page updated on June 28, 2007

 


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