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In the early 17’th century, Johannes Kepler presented the groundbreaking idea that planetary orbits were elliptical in shape. The idea was immediately met with outrage by the broader scientific community who argued that our solar system could not possibly be composed of such imperfect, and initially indescribable, figures (Hawking and Mlodinow, 2005). Astronomers now know that Kepler was right. With modern technology, scientists proved this theory and discovered other previously unknown shapes existing in our solar system (Levy, 2009). In particular, they realized that certain figures appear to play a big part in modeling our stellar surroundings: the ellipse, the circle, the parabola, and the hyperbola. Even more crucially, mathematicians have developed ways to describe and reproduce these universally important shapes, collectively known as the Conic Sections. As the name implies, the conic sections can all be produced by manipulating a cone. As will be described more thoroughly, depending on the angle to the cone’s base at which a plane intersects the cone, the cross-section will produce either a circle, ellipse, hyperbola, or parabola. Each of these conic sections can be modeled by an equation that reflects the various components of the shape

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17世紀初頭、ヨハネス・ケプラーは惑星の軌道が楕円形であるという画期的な考えを提示した。このアイデアはすぐに、私たちの太陽系がこのような不完全で、最初は説明できない人物で構成される可能性はないと主張したより広範な科学界から憤慨を受けた（ Hawking and Mlodinow, 2

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In the early 17th century, Johannes Kepler presented the groundbreaking idea that the orbit of a planet was oval. The idea was immediately outraged by the wider scientific community, who argued that our solar system could not be made up of such incomplete, initially inexplicable figures (cf.

INTO JAPANESE

17世紀初頭、ヨハネス・ケプラーは惑星の軌道が楕円であるという画期的な考えを提示した。このアイデアは、私たちの太陽系がこのような不完全で、最初は不可解な数値で構成されることはできないと主張した、より広い科学界にすぐに憤慨されました（参照：

BACK INTO ENGLISH

In the early 17th century, Johannes Kepler presented the groundbreaking idea that the orbit of a planet was elliptical. The idea was immediately resented by the wider scientific community, who argued that our solar system could not be composed of such imperfect, initially mysterious numbers (cf.

INTO JAPANESE

17世紀初頭、ヨハネス・ケプラーは惑星の軌道が楕円であるという画期的な考えを提示した。このアイデアはすぐに広範な科学界から恨まれ、私たちの太陽系はこのような不完全で、最初は神秘的な数で構成されることはできないと主張しました（ cf.

BACK INTO ENGLISH

In the early 17th century, Johannes Kepler presented the groundbreaking idea that the orbit of a planet was elliptical. The idea was immediately resented by the wider scientific community, who argued that our solar system could not be composed of such imperfect and mysterious numbers at first (cf.

INTO JAPANESE

17世紀初頭、ヨハネス・ケプラーは惑星の軌道が楕円であるという画期的な考えを提示した。このアイデアはすぐに広範な科学界から恨まれ、我々の太陽系は最初はそのような不完全で神秘的な数字で構成されることはできないと主張しました（参照：

BACK INTO ENGLISH

In the early 17th century, Johannes Kepler presented the groundbreaking idea that the orbit of a planet was elliptical. The idea was immediately resented by the wider scientific community, who argued that our solar system could not initially consist of such incomplete and mysterious numbers (cf.

INTO JAPANESE

17世紀初頭、ヨハネス・ケプラーは惑星の軌道が楕円であるという画期的な考えを提示した。このアイデアはすぐに広い科学界から恨まれ、私たちの太陽系は最初はそのような不完全で神秘的な数で構成されることはできないと主張しました（ cf.

BACK INTO ENGLISH

In the early 17th century, Johannes Kepler presented the groundbreaking idea that the orbit of a planet was elliptical. The idea was immediately resented by the wider scientific community, who argued that our solar system could not initially consist of such incomplete and mysterious numbers (cf.