The History of Geometric Construction

The History of Geometric Construction By: Morgan Hungerford

Geometry’s Beginning Geometry is believed to have originally started in ancient Mesopotamia, Egypt around 3000 BC.

Euclid Euclid, an Alexandrian Greek Mathematician, was one of the first men to experiment with geometric constructions. He created several postulates that still define constructions today. He is accredited with the foundation of modern-day Euclidean geometry. Euclid lived in Alexandria, Egypt.

Elements Euclid is credited with writing a work called Elements that is the basis of some key ideas in geometry even today. This work tells of Euclid’s 10 axioms, and other vital geometric ideas.

Tools Ancient Geometricians used compasses and straightedges just as we do today, though compasses have changed slightly since the time of Euclid, in 300 B.C. They were previously spring loaded and would close when not pressed on a paper but are now simply adjustable.

Uses The ancient people discovered geometric constructions to meet their needs. The Greeks did only had whole numbers and had no zero at all. This made it very hard for them to do arithmetic so other ways were discovered. They experimented with lengths, angles, areas, and volumes, and these eventually led to uses in surveying, construction, and even astronomy.

Today Geometric constructions are not much different today as they were in Euclid’s time. Only the means with which we create geometric constructions has been drastically altered. Electronic programs have been developed to assist us and tools and purposes have been changed but remarkably, the rules we follow are almost exactly the same.

Constructing a Perpendicular Bisector By: Morgan Hungerford

Step one Use a straightedge to make a line. Put points on the ends and label them A and B. A B

Step two Put the compass pencil point on point A and the sharp point on the line. Adjust the compass so that it is wider than half of line AB. A B

Step three Without changing the width of the compass, construct a circle. A B

Step four Leaving the compass the same width, put the compass pencil point on point B and the sharp point on the line. A B

Step Five Without changing the width of the compass, construct a circle. A B

Step six Label the two points where the circles intersect; C and D. C A B D

Step seven Use a straight edge and draw a line between points C and D. C A B D

Step eight Label the line you just drew; E. This is your perpendicular bisector. C A B D E

The History of Geometric Construction