Creation of Conic Sections
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Creation of Conic Sections
By Brandi Bowden
Menaechmus was an ancient Greek mathematician born in Alopeconnesus(modern day Turkey), who is known for his friendship with the philosopher Plato, as well his apparent discovery if conic sections. He also is known for his solution of the, at the time, long standing problem of the ‘doubling the cube’ using the parabola and hyperbola.
To ‘double the cube’ means to be given a cube of some side length so that s and the volume V, and to construct a new cube, larger than the first, with volume 2V and therefore side length s times 3 times the square root of two. The problem is known to be impossible to solve with only a compass and straight edge, because three times the square root of two is not a constructible number. The correct interpretation was that one must double the volume of their altar, not merely its side length. This proved to be a very difficult problem, but was solved in 350 BC thanks to the efforts of Menaechmus with use of parabolas and hyperbolas.
Menaechmus is also remembered for his discovery of conic sections. Menaechmus is credited with the discovery of the ellipse, the parabola, and the hyperbola, in order to solve the ‘doubling of the cube’. Menaechmus knew that in a parabola y squared is equal to lx, where l is a constant called the latus rectum, although he was not aware of the fact that any equation in two unknowns determines a curve. He apparently came up with these properties of conic sections and others as well. It was with this information that he was able to find the solution to the problem that had troubled mathematicians for eighty years, at the time.
By Brandi Bowden
Menaechmus was an ancient Greek mathematician born in Alopeconnesus(modern day Turkey), who is known for his friendship with the philosopher Plato, as well his apparent discovery if conic sections. He also is known for his solution of the, at the time, long standing problem of the ‘doubling the cube’ using the parabola and hyperbola.
To ‘double the cube’ means to be given a cube of some side length so that s and the volume V, and to construct a new cube, larger than the first, with volume 2V and therefore side length s times 3 times the square root of two. The problem is known to be impossible to solve with only a compass and straight edge, because three times the square root of two is not a constructible number. The correct interpretation was that one must double the volume of their altar, not merely its side length. This proved to be a very difficult problem, but was solved in 350 BC thanks to the efforts of Menaechmus with use of parabolas and hyperbolas.
Menaechmus is also remembered for his discovery of conic sections. Menaechmus is credited with the discovery of the ellipse, the parabola, and the hyperbola, in order to solve the ‘doubling of the cube’. Menaechmus knew that in a parabola y squared is equal to lx, where l is a constant called the latus rectum, although he was not aware of the fact that any equation in two unknowns determines a curve. He apparently came up with these properties of conic sections and others as well. It was with this information that he was able to find the solution to the problem that had troubled mathematicians for eighty years, at the time.