Girih patterns can be created in a variety of ways, including the traditional compass and Straightedge;
One of the things that makes isometric drawings so attractive is the ease
with which 60° angles can be constructed with only a compass and Straightedge.
One of the things that makes isometric drawings so attractive is the ease
with which 60 degree angles can be constructed with only a compass and Straightedge.
The Ancient Greeks had shown that regular
3, 5, and 15-sided polygons can be constructed using only a Straightedge and compass,
but had not been able to discover any more such shapes.
If you need to scribe a line on your project material, a marking gauge will let you lay things out without the many steps involved in measuring off multiple marks and
connecting them with a Straightedge.
Mathematicians thus accepted his belief that geometry should use no tools but compass and Straightedge- never measuring instruments such as a marked ruler
or a protractor, because these were a workman's tools, not worthy of a scholar.
Other 19th-century mathematicians utilized this in their proofs that Straightedge and compass alone are not sufficient
to trisect an arbitrary angle, to construct the side of a cube twice the volume of a given cube, nor to construct a square equal in area to a given circle.
This dictum led to a deep study of possible compass and Straightedge constructions, and three classic construction problems:
how to use these tools to trisect an angle, to construct a cube twice the volume of a given cube, and to construct a square equal in area to a given circle.