Thiele's interpolation formula: Difference between revisions

{{task|Arithmetic operations}}

In [[wp:mathematics|mathematics]], '''[[wp:Thiele's_interpolation_formula|Thiele's interpolation formula]]''' is an [[wp:interpolation formula|interpolation formula]] for a function ''f''(•) of a single variable, due to the [[wp:Denmark|Danish]] [[wp:mathematician|mathematician]] [[wp:Thorvald N. Thiele|Thorvald Nicolai Thiele]]. It is expressed as a [[wp:continued fraction|continued fraction]], where ρ represents the [[wp:reciprocal difference|reciprocal difference]]:

 

Demonstrate Thiele's interpolation function by:

# Building a ''trig table'' of values of the trig functions ''sin'', ''cos'' and ''tan'' for x from 0 to 1.55;

# Finally: demonstrate the following well known trigonometric identities:

#* 6 × sin^-1 ½ = π