Ruler And Compass
AllPages
RecentChanges
Links to this page
Edit this page
Search
Entry portal
Advice For New Users
Ancient Greek mathematicians (and many others since) felt that there was something fundamental about straight lines and circles, so they were very interested in what geometrical constructions could be done using those. Solving a problem in plane geometry with "ruler and compass" (it should really be "straightedge and compass" since you aren't supposed to use the markings on the ruler) means solving it using only the following operations:

1. Given two points, draw the straight line passing through both of them.

2. Given two (non-parallel) straight lines, find the point where they intersect.

3. Given two points, draw the circle with one as centre and passing through the other.

4. Given two circles, or a circle and a straight line, find the point or points (if any) where they intersect.

Some problems can be solved using only these operations and some can't. For instance, you can do these:

a1. Given a triangle, find a square of equal area.

b1. Construct a regular polygon with 102 sides.

but you can't do these:

a2. Given a circle, find a square of equal area.

b2. Construct a regular polygon with 100 sides.

How to distinguish the possible problems from the impossible? That's a task for the (at first glance quite unrelated) field of Galois theory...

Links to this page / Page history / Last change to this page
Recent changes / Edit this page (with sufficient authority)
All pages / Search / Change password / Logout