Hypsicles ( grc-gre, Ὑψικλῆς; c. 190 – c. 120 BCE) was an ancient
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
known for authoring ''On Ascensions'' (Ἀναφορικός) and the Book XIV of
Euclid's ''Elements''. Hypsicles lived in
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandri ...
.
Life and work
Although little is known about the life of Hypsicles, it is believed that he authored the astronomical work ''On Ascensions''. The mathematician
Diophantus
Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the aut ...
of Alexandria noted on a definition of polygonal numbers, due to Hypsicles:
On Ascensions
In ''On Ascensions'' (Ἀναφορικός and sometimes translated ''On Rising Times''), Hypsicles proves a number of propositions on
arithmetical progressions and uses the results to calculate approximate values for the times required for the
signs of the zodiac
The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The path ...
to rise above the
horizon
The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether i ...
. It is thought that this is the work from which the division of the
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
into 360
parts may have been adopted
since it divides the day into 360 parts, a division possibly suggested by
Babylonian astronomy,
although this is mere speculation and no actual evidence is found to support this.
Heath
A heath () is a shrubland habitat found mainly on free-draining infertile, acidic soils and characterised by open, low-growing woody vegetation. Moorland is generally related to high-ground heaths with—especially in Great Britain—a cooler a ...
1921 notes, "The earliest extant Greek book in which the division of the circle into 360 degrees appears".
Euclid's Elements
Hypsicles is more famously known for possibly writing the Book XIV of Euclid's ''Elements''. The book may have been composed on the basis of a treatise by
Apollonius. The book continues Euclid's comparison of
regular solids inscribed
{{unreferenced, date=August 2012
An inscribed triangle of a circle
In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "figure F is inscribed in figu ...
in
spheres
The Synchronized Position Hold Engage and Reorient Experimental Satellite (SPHERES) are a series of miniaturized satellites developed by MIT's Space Systems Laboratory for NASA and US Military, to be used as a low-risk, extensible test bed for the ...
, with the chief result being that the ratio of the surfaces of the
dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
and
icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
inscribed in the same sphere is the same as the
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of their
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
s, the ratio being
.
Heath further notes, "Hypsicles says also that Aristaeus, in a work entitled ''Comparison of the five figures'', proved that the same circle circumscribes both the pentagon of the dodecahedron and the triangle of the icosahedron inscribed in the same sphere; whether this Aristaeus is the same as the Aristaeus of the Solid Loci, the elder (
Aristaeus the Elder
Aristaeus the Elder ( grc-gre, Ἀρισταῖος ὁ Πρεσβύτερος; 370 – 300 BC) was a Greek mathematician who worked on conic sections. He was a contemporary of Euclid.
Life
Only little is known of his life. The mathematician Pa ...
) contemporary of Euclid, we do not know."
Hypsicles letter
Hypsicles letter was a preface of the supplement taken from Euclid's Book XIV, part of the thirteen books of
Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postu ...
, featuring a treatise.
Notes
References
*
*
External links
The mac-tutor biography of Hypsicles
{{Authority control
Ancient Greek astronomers
Ancient Greek mathematicians
2nd-century BC Greek people
190s BC births
120s BC deaths
2nd-century BC mathematicians