Editing Gottfried Wilhelm Leibniz (section)

===Geometry===
The [[Leibniz formula for π|Leibniz formula for {{pi}}]] states that
:<math>1 \,-\, \frac{1}{3} \,+\, \frac{1}{5} \,-\, \frac{1}{7} \,+\, \cdots \,=\, \frac{\pi}{4}.</math>
Leibniz wrote that circles "can most simply be expressed by this series, that is, the aggregate of fractions alternately added and subtracted".<ref>{{cite book|last1=Jones|first1=Matthew L.|title=The Good Life in the Scientific Revolution : Descartes, Pascal, Leibniz, and the Cultivation of Virtue|date=2006|publisher=Univ. of Chicago Press|location=Chicago [u.a.]|isbn=978-0-226-40954-2|page=169|edition=[Online-Ausg.]}}</ref> However this formula is only accurate with a large number of terms, using 10,000,000 terms to obtain the correct value of {{sfrac|{{pi}}|4}} to 8 decimal places.<ref>{{cite book|last1=Davis|first1=Martin|title=The Universal Computer : The Road from Leibniz to Turing, Third Edition|date=2018-02-28|publisher=CRC Press|isbn=978-1-138-50208-6|page=7}}</ref> Leibniz attempted to create a definition for a straight line while attempting to prove the [[parallel postulate]].<ref>{{cite book|last1=De Risi|first1=Vincenzo|title=Leibniz on the Parallel Postulate and the Foundations of Geometry|date=2016|isbn=978-3-319-19863-7|page=4|publisher=Birkhäuser }}</ref> While most mathematicians defined a straight line as the shortest line between two points, Leibniz believed that this was merely a property of a straight line rather than the definition.<ref>{{cite book|last1=De Risi|first1=Vincenzo|title=Leibniz on the Parallel Postulate and the Foundations of Geometry|date=10 February 2016|publisher=Birkhäuser, Cham|isbn=978-3-319-19862-0|page=58}}</ref>