Hypsicles facts for kids

Hypsicles (born around 190 BCE, died around 120 BCE) was an ancient Greek mathematician and astronomer. He is known for writing a book called On Ascensions. He might also have written Book XIV of Euclid's famous Elements. Hypsicles lived in the city of Alexandria.

Life and Discoveries

We don't know much about Hypsicles' life. But it is believed he wrote an astronomy book called On Ascensions. Another mathematician, Diophantus, mentioned Hypsicles' ideas about special numbers called polygonal numbers. These numbers are formed by adding up numbers in a certain pattern.

About On Ascensions

In his book On Ascensions, Hypsicles wrote about arithmetic progressions. These are lists of numbers where each number increases by the same amount. He used these ideas to figure out how long it takes for the signs of the zodiac to appear above the horizon.

This book might be where the idea of dividing a circle into 360 degrees came from. It divides the day into 360 parts. This way of dividing things might have come from Babylonian astronomy. But we don't have clear proof of this. Still, On Ascensions is the oldest Greek book we know that uses the 360-degree circle. It also seems to be the first Greek text to use the Babylonian idea of dividing the zodiac into 12 signs, each with 30 degrees.

Hypsicles and Euclid's Elements

Hypsicles is perhaps most famous for possibly writing Book XIV of Euclid's Elements. Euclid's Elements is a very important math book. Book XIV might have been based on earlier writings by Apollonius.

This book continues Euclid's work on comparing regular solids placed inside spheres. Regular solids are 3D shapes with all sides and angles the same, like a cube. A key idea in Book XIV is that for a dodecahedron (a 12-sided shape) and an icosahedron (a 20-sided shape) placed inside the same sphere, the way their surfaces compare is the same as the way their volumes compare.

The historian Thomas Heath also noted that Hypsicles mentioned another mathematician, Aristaeus. Aristaeus supposedly showed that the same circle can go around both the pentagon of a dodecahedron and the triangle of an icosahedron, if they are in the same sphere.

Hypsicles' Letter

Hypsicles also wrote a letter that served as an introduction to a part of Euclid's Book XIV. In this letter, Hypsicles wrote to a friend named Protarchus. He explained that his father and another mathematician, Basilides of Tyre, had looked at a book by Apollonius. This book was about comparing the dodecahedron and icosahedron when they are inside the same sphere.

Hypsicles said that his father and Basilides thought Apollonius's first ideas on this topic were not quite right. So, they tried to fix and rewrite it. Later, Hypsicles found another book by Apollonius that had a better explanation of the problem. Hypsicles was very impressed by Apollonius's new work.

Hypsicles decided to write his own comments on the topic. He wanted to share his thoughts with Protarchus because Protarchus was good at math, especially geometry. Also, Protarchus was a good friend of Hypsicles' father and was kind to Hypsicles himself.