Euler's equation

(where a, b are fixed limits) with each of a family of graphs y(x); this functional might represent the arc length of such graphs, the time taken to travel along the graphs under gravity, etc. Euler's equation then states I is maximal when

As an example, the arc length of a curve y(x) from (a,c) to (b,d) is

so that and Euler's equation then reads

Integrating and rearranging we find that y′ is constant, and so the graph of y is a straight line.

• finitely generated
• finite population correction
• finite‐dimensional
• finitism
• first derivative
• first fundamental form
• first isomorphism theorem
• first-order logic
• first principles
• first‐order differential equation
• Fisher's exact test
• Fisher, Sir Ronald Aylmer
• fit
• fixed point
• fixed-point theorem
• fixed‐point iteration
• fixed‐point notation
• flag
• flat angle
• flex
• floating‐point notation
• float of an activity
• floor
• fluent
• fluid mechanics