Everyone Knows What a Curve Is
Felix Klein's quote, illustrated by the first steps toward a Weierstrass-style function that wiggles more at every scale.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2024-01-01-everyone-knows-what-a-curve-is/ (CC BY-NC 4.0)Transcript
"Everyone knows what a curve is, until he has studied enough mathematics." – Felix Klein
Step 1: f(x) = cos(πx) · Step 2: f(x) = cos(πx) + cos(21πx)/3 · Step 3: f(x) = cos(πx) + cos(21πx)/3 + cos(441πx)/9 [zoom: "each apparent 'peak' in Step 3 is actually 21 peaks too skinny to see"]