Apollonius of Perga

Long ago, a man named Apollonius studied shapes.

He looked at how a flat plane can cut a cone.

Cutting the cone in different ways makes new shapes. If you cut it one way, you get a circle.

Other ways make shapes called an ellipse, a parabola, or a hyperbola.

He gave these shapes their names. We still use his names today!

Apollonius also looked at the stars. He studied how planets move in space.

He was a very great thinker. Today, a crater on the Moon bears his name.

Apollonius of Perga was a great Greek thinker.

He lived a long time ago. He studied math and the stars. Most people know him for his work on shapes. These shapes come from cutting a cone with a flat plane.

If you cut a cone in different ways, you get new shapes. He gave these shapes their names. We still use his names today. They are the ellipse, the parabola, and the hyperbola.

He used a special way to study the parabola. He looked at how areas of shapes worked together.

Apollonius also studied how planets move. He thought they moved in special paths. Many people believed his ideas for a long time. Most of his books are lost now. Only one major work, called Conics, survived.

We still have parts of his work in other languages. Today, a crater on the Moon is named after him. This honors his big ideas in math.

Apollonius of Perga was a famous Greek mathematician and astronomer.

He lived a very long time ago in the ancient world. He is most famous for his work on shapes called conic sections. These shapes are made by cutting a cone with a flat surface. He built upon the ideas of earlier thinkers like Euclid and Archimedes. His work was so important that it lasted for many centuries. Even today, we use the names he created for these shapes.

To understand his work, imagine a cone. If you slice through the cone at different angles, you get different shapes. A slice parallel to the base creates a perfect circle. If you tilt the slice, you might get an ellipse.

A different angle can create a parabola or a hyperbola. Apollonius defined these three shapes very clearly. He used a method called the "application of areas" to study them.

This was a way to see how the area of a rectangle related to a square. This helped him describe the math behind the parabola.

We do not know the exact dates of his life. However, we know he lived around the time of Ptolemy III Euergetes. This king ruled Egypt from 246 to 222 BC. Because of this, scholars think Apollonius was likely born after 246 BC. He was likely from the city of Perga in Pamphylia.

He probably studied and wrote his books in the city of Alexandria. This city was a huge center for learning and science back then.

Apollonius wrote many books, but most are now lost to time. His most famous work is called "Conics." This work is divided into eight books. Only the first four books exist as original Greek texts. Some of the other books were saved through Arabic translations.

He also wrote about astronomy and the movement of planets. He had a theory about how planets move in paths called eccentric orbits. People believed his idea for a very long time until the Renaissance.

His ideas still connect to the math you might see in school today. The way he organized his proofs is like a modern math textbook. He would list what was given and then prove a new fact. His work on shapes is used in many types of science. Even the moon carries his name in a special way. There is a crater on the Moon called the Apollonius crater.

This honors the amazing things he discovered long ago.

Apollonius of Perga was a monumental Greek geometer and astronomer.

He is most famous for his study of conic sections. These are two-dimensional shapes created by the intersection of a plane and a cone. Apollonius built upon the foundational work of Euclid and Archimedes. He brought the study of these shapes to a level of sophistication that lasted until the invention of analytic geometry. His specific definitions for the ellipse, parabola, and hyperbola remain the standard in mathematics today. Because of his massive influence, he is considered one of the greatest mathematicians of antiquity.

To understand his work, one must visualize the mechanism of a conic section.

A conical surface is generated by rotating a line segment around a bisector point. The endpoints of this segment trace circles in different planes. A single cone is one branch of this double conical surface. It consists of an apex, or vertex, a base, and an axis. A section occurs when an imaginary plane cuts through this cone. If the plane passes through the vertex, the resulting section is a triangle. If the plane is parallel to the base, the section is a circle.

Apollonius categorized the different types of sections based on the angle of the cut.

An ellipse is formed when the plane is inclined to the base. The angle of this plane must be greater than zero but less than the angle of the cone's side. A parabola occurs when the cutting plane is parallel to the side of the cone. A hyperbola is created when the plane is parallel to the axis. This type of cut intersects both cones in a double conical surface, resulting in two distinct branches.

He also developed a specialized method called the "application of areas" to describe these shapes.

This method was used to establish mathematical relationships without modern algebraic symbols. For a parabola, he asked if a rectangle formed by certain segments would equal the area of a specific square. If the rectangle matched the square, the shape was a parabola. If the rectangle was smaller, the shape was an ellipse. If the rectangle was larger, the shape was a hyperbola. He used terms like "deficit" and "surfeit" to describe these differences in area.

Very little is known about the personal life of Apollonius. We can estimate his era through the writings of the 6th-century commentator Eutocius of Ascalon. Eutocius noted that Apollonius was from Perga in Pamphylia. He likely lived during the reign of Ptolemy III Euergetes, who ruled Egypt from 246 to 222 BC. This suggests Apollonius was born after 246 BC. While he was from Perga, evidence suggests he lived and studied in Alexandria. This city was a major center for Hellenistic culture and scientific research.

Apollonius was a prolific writer, yet much of his work has been lost.

His most important surviving work is titled *Conics*. This text is divided into eight books. Only the first four books survive as original Greek texts. Books five through seven are only known through an Arabic translation by Thābit ibn Qurra. The status of the eighth book is uncertain, though fragments exist. He also wrote on astronomy, proposing that planets move in eccentric orbits. This hypothesis was widely accepted until the Renaissance changed our understanding of the solar system.

His mathematical style was highly structured and influenced later teaching methods.

In *Conics*, he used a system of definitions and propositions to be proved. This arrangement is very similar to how modern geometry textbooks are organized today. His work connects geometry to the broader study of the heavens through his astronomical theories. Even today, his legacy is visible in the stars. A crater on the Moon is named the Apollonius crater to honor his contributions to science.