>> Mathematicians have a habit of studying, just for the fun of it, things that seem utterly useless; then centuries later their studies turn out to have enormous scientific value....!
In this section, we have to discuss about 'Conic Sections' especially trying to simply introduce - How developed the 'Conic Sections' concept's is?
How developed the 'Conic Sections' Concepts:
Conic sections is among the oldest curve, and is an old mathematics topics studied symmetrically & thoroughly.
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| Fig: Conic Section |
Menaechmus (380-320 BC) was the ancient Greek mathematician, who
1st construction involving a 'Cone' in mind to solved the problem of 'doubling the cube'. He developed the properties of conic section by using the concept 'cutting of a cone'. But he did not use the term 'Parabola' & 'Hyperbola' to deal with such types of curve. Instead of these, he called 'section of a right-angled cone' for parabola & 'section of an obtuse-angled cone' for hyperbola. [Remind that: these term 'parabola' & 'hyperbola' are named as by Apollonius].
After Menaechmus, Aristaeus & Euclid formalized & expanded upon the 'Conics' through their written books. They wrote various types of books (of solid loci) connected with the 'Conics'.
Then came the greatest Archimedes, who used the elementary theory of conic sections to developed important concepts about parabolas.
Apollonius (262-190 BC) was the greatest ancient Greek mathematician, who consolidated & extended previous results of conics into a monograph conic sections, consisting of eight books with 487 propositions. He also completed the four books of 'Euclid's Conics'. He was the first, to base the theory of all three conics (ellipse, parabola & hyperbola) on sections of one circular cone, right or oblique. He also named the conic sections as: Ellipse, Parabola & Hyperbola.
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| Fig: Kepler's planets orbit |
After Apollonius, the Conic Sections theory disappeared for over 1000 years; No any important scientific applications were found until
17th century. After
17th century, Kepler & Galileo helps to develop the 'Conic Sections' by using for scientific approach.
Kepler derived his first
law of planetary motion(1609). He discovered that Planets move in elliptical path with the Sun at one focus. Galileo proved that projectiles travel in parabolas - in his
Dialogues of the Two New Sciences(1638). They used to powerful modeling tools (i.e. Conics) for explaining the physical laws of the universe.
In 1639, the French engineer Girard Desargues initiated the study of those properties of conics that are invariant under projections (See:
Projective geometry). In
18th century, architects created a fad for
Whispering galleries - such as in the St. Paul's Cathedral in London - in which a Whisper at one focus of an ellipsoid can be heard at the another focus, but cannot be heard at many places in between.
Likewise, now-days new application for conic sections continue to be found. (See more in:
Conic Sections & its Importance)
After then everybody knows that - How powerful & how useful these 'Conic Sections theory' is?
