Geometry

Pronunciation: /dʒiˈɒ.mɪ.tri/ Explain

Geometry is the study of points, lines, and shapes in space¹. Each branch of geometry is defined by the basic assumptions, or axioms, of that geometry. All other properties and theorems are derived from these basic assumptions.

Classic Euclidean geometry has five basic assumptions or axioms:

1. Any two points can be joined by a straight line.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must each other on that side if extended far enough.

For more information on the axioms of Euclidean Geometry, see Elements Book I by Euclid. Translated by D. Joyce.

Plane geometry is the study of objects in a 2-dimensional space. Solid geometry is the study of objects in a 3-dimensional space.

References

1. McAdams, David E.. All Math Words Dictionary, geometry. 2nd Classroom edition 20150108-4799968. pg 85. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 1. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 7/11/2018. http://www.archive.org/stream/mathengineer00kellrich#page/1/mode/1up/search/geometry. Buy the book
3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. Introduction. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 7/11/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/n18/mode/1up/search/geometry. Buy the book
4. Descartes, René. La géométrie. Translated by A. Hermann. www.archive.org. Librarie Scientifique. 1886. Last Accessed 7/11/2018. http://www.archive.org/stream/lagomtrie00descuoft#page/n8/mode/1up. Buy the book

More Information

• Euclid. Elements. 3/12/2009. http://babbage.clarku.edu/~djoyce/java/elements/toc.html.
• Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.

Educator Resources

• Surveying and Geometry. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Eom-SurveyingAndGeometry/index.htm.
• Surveying and Studying Mars. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Eom-SurveyingAndStudyingMars/index.htm.
• Pythagoras Theorem and Ellipses. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Goe-PythagorasTheoremAndEllipses/index.htm.

Cite this article as:

McAdams, David E. Geometry. 3/14/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/g/geometry.html.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/10/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
3/14/2018: Clarified wording. Added vocabulary links. (McAdams, David E.)
12/15/2009: Added "References". (McAdams, David E.)
8/4/2008: Added More Information. Added reference to Elements, vocabulary links (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)