Shapes by the Numbers
Coordinate Geometry
Sketch 16
Kristina and Jill
Overview of contributions
Ancient times
Early mathematicians (16th century and
earlier)
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Menaechmus
Apollonius
Francois Viete
Major Contributors
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Descartes
Fermat
Ancient Times
Uses
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Egypt
Rectangular grid
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Rome
Surveyors
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Greece
Mapmakers
Early Mathematicians
Menaechmus
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Introductions of Conic Sections
Apollonius
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Work related to loci
Made a start in the development of analytic geometry
Related geometric figures to ratios and words
Francois Viete
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Took a leap on focusing algebra to geometric
problems
Fermat
Study works of Apollonius and Viete
He wrote a manuscript entitle Introduction to Plane and
Solid Loci
Developed a unique coordinate system
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His development of locus to equation
Represented curves using algebra in two variables
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Parabola: x2=dy
Hyperbola: b2+x2=ay2
Circle: b2-x2=y2
Ellipse: b2-x2=ay2
Straight line: x2±xy=ay2
Only considered positive values
His contributions were not published until after his death
so a lot of credit was given to Descartes.
Descartes
Influenced by Viete and Islamic mathematicians
Published Discourse on the Method of Rightly
Conducting the Reason in the Search for Truth in the
Sciences

La Geometrie is the section in which his work on analytic
geometry appears.
Used single horizontal axis
Introduced what we now know as x and y

Represented unknowns using the letters at the end of alphabet
and constants using letters at the beginning of the alphabet
Demonstrated how algebraic equations are formed using
their solutions
Others that followed
Frans van Schooten

Translated Descartes work into Latin and added
missing detail
John Wallis

Extended analytic geometry ideas to include
negatives
Jan de Witt
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Details on how to solve the locus problem for
quadratic equations
Isaac Newton
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Learned about analytic geometry on his while
developing ideas of Calculus
Compare and Contrast
Fermat
Described curve from an
equation
Used a single axis
(horizontal)
Never published his work
Descartes
Described algebraic
equation from a curve
Used a single axis
(horizontal)
Published his work but in
French with omitted detail
Dealt with more complex
equations than Fermat
did
History of Geometry and Algebra
Algebra grew out of simple manipulation of
geometric shapes
During the medieval period and
Renaissance algebra was freed from
Geometry
Algebra and Geometry returned to one
another in what we now know as analytic
geometry
Timeline
Ancient Egypt used rectangular grid
Same method used by Roman Surveyors
and Greek mapmakers
350 B.C. Menaechmus introduces conic
sections
Approximately 250 B.C. Apollonius works
on loci of curves
Late 16th Century Francois Viete worked
on using algebra in geometric problems
Timeline Continued
Early 17th Century Fermat and Descartes
introduced work on analytic geometry
1649-1693 Van Schooten translated La
Geometrie into Latin and added omitted detail
Approximately 1659 Jan de Witt provided details
to solve locus problems of quadratic equations
End of the 17th Century analytic geometry was
widely known throughout Europe
Resources
Berlinghoff, William P., and Fernando Q. Gouvea. Math
Through the Ages: a Gentle History for Teachers and
Others. Farmington, Maine: Oxton House, 2002. 135140.
Katz, Victor J. A History of Mathematics. New York:
Pearson, 2004. 260-270.
"Analytic Geometry: Marriage of Algebra & Geometry."
Think Quest. 2001. 14 Nov. 2006
<http://library.thinkquest.org/C0110248/geometry/history
5.htm>.
Gale, Thomas. "The Development of Analytic Geometry."
Book Rags. 2006. Science and Its Times. 14 Nov. 2006
<http://www.bookrags.com/research/the-development-ofanalytic-geometr-scit-03123/>.