
Universal chord theorem
Guarantees chords of length 1/n exist for functions satisfying certain conditions

Guarantees chords of length 1/n exist for functions satisfying certain conditions
In mathematical analysis, the universal chord theorem states that if a function f is continuous on [a,b] and satisfies f ( a ) = f ( b ) {\displaystyle f(a)=f(b)} , then for every natural number n {\displaystyle n} , there exists some x ∈ [ a , b ] {\displaystyle x\in [a,b]} such that f ( x ) = f ( x + b − a n ) {\displaystyle f(x)=f\left(x+{\frac {b-a}{n}}\right)} .
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