File:Parallel_postulate_en.svg · Wikimedia Commons · See Wikimedia Commons
parallel postulate
Sign in to saveAlso known as Euclid's fifth postulate, fifth postulate
axiom in Euclidean geometry
Wikidata facts
- Image
- Parallel postulate en.svg
Show 1 more fact
- Commons category
- Parallel postulate
Sources (3)
via Wikidata · CC0
~18 min read
Article
If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate is the fifth postulate in Euclid's Elements and a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If a straight line intersects two other straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Gallery (4)
Connections
Pythagorean theorem
Entity
axiom
Entity
Elements
Entity
Diophantus of Alexandria
Entity
non-Euclidean geometry
Entity
Giovanni Girolamo Saccheri
Entity
elliptic geometry
Entity
mathematics in medieval Islam
Entity
independence
Entity
Rome
Entity
Aristotle
Entity
Archimedes
Entity
number
Entity
geometry
Entity
Pythagoras
Entity
Euclid
Entity
Carl Friedrich Gauss
Entity
arithmetic
Entity
triangle
Entity
Arthur Schopenhauer
Entity