Crinkled arc
id:
crinkled-arc-248-8827408
title:
Crinkled arc
text:
In mathematics, and in particular the study of Hilbert spaces, a crinkled arc is a type of continuous curve. The concept is usually credited to Paul Halmos. Specifically, consider f : [ 0 , 1 ] → X , where X is a Hilbert space with inner product ⟨ ⋅ , ⋅ ⟩ . We say that f is a crinkled arc if it is continuous and possesses the crinkly property: if 0 ≤ a < b ≤ c < d ≤ 1 then ⟨ f − f , f − f ⟩ = 0 , that is, the chords f − f and f − f are orthogonal whenever the intervals [ a , b ] and [ c , d ] ar
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Crinkled_arc
date created:
date modified:
2024-01-28T01:17:01Z
main entity:
{"identifier":"Q56291792","url":"https://www.wikidata.org/entity/Q56291792"}
image:
fields total:
13
integrity:
13