Discovered around 350 BCE, Greek mathematician Menaechmus discovered "conic sections", special curves that he apparently used to solve the problem of doubling the cube. They were called so because they were done by slicing a cone with a flat plane. One cone is formed by straight line segments extending for a single point and passing through a circle (base). Double cones could also be created by extending the line segments through the point rather than just ending there. A double cone would appear as two ice cream cones that are joined by their pointy ends.
These conic sections could be used to solve certain cubid equations. There are three main types which can be classified as the ellipse, parabola, and hyperbola. When a plane passes through the cone at an angle it forms a closed oval curve called an ellipse. If the plane slices exactly perpendicular to the cones axis then it forms a circle, which is a special kind of ellipse. When the plane cuts parallel to one of the lines on the surface of the cone then a parabola is formed (a single open curve). Lastly, when a plane cuts through both halves of a double cone. a hyperbola is formes (two symmetrically related open curves). Here we can see how we get asymptotes.
In todays mathematics and applied science, these curves are extremely important. The planets in our solar system orbit in the shape of an elipse.
"This eliptical orbit in one of the observations that led Newton to formulate
his famous "inverse square law" of gravity. This in turn led to the
realization that some aspects of the universe exhibit clear mathematical
patterns. It opened up the whole of astronomy by making planetary
phenomena computable."
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