Second-order interpolation
AI-drafted · awaiting admin review
Brahmagupta (665 CE) used a second-order interpolation rule to fill in sine tables, about 1,000 years before the equivalent Newton–Stirling formula in Europe.
Independent discoveriesMathematics & astronomy
Indian claim
Brahmagupta discovered the Newton–Stirling interpolation formula a thousand years before Newton.
Evidence for the Indian claim
- A verse in Brahmagupta's Khandakhadyaka (665 CE) gives a rule using the past and coming differences of a table, equivalent to the second-order Newton–Stirling formula.
- Later Indian astronomers such as Govindasvamin and Madhava refined such rules.
Commonly credited to
Interpolation formulas are named after Newton and James Stirling, who developed the general theory of finite differences.
Evidence for the other claim
- Newton and Stirling gave general formulas of any order, not just second order.
- In China, the astronomer Liu Zhuo used second-order interpolation in his calendar of about 600 CE, independently.
What historians and scientists say
Brahmagupta's second-order rule is far earlier than the European formula. Similar methods also appeared in China; the general theory came later in Europe.