Phantom Graphs Background. Notes on creating phantom graphs.

Phantom Graphs Background. Notes on creating phantom graphs.

Phantom Graph of ellipse is hyperbola (& v.v.)

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ellipse-hyperbola

Phantom Graph of exp(x)

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Howard K. Fehr's notes

A readable if not perfect pdf copy of the section from Fehr that describes this technique. (1951) Fehr was head of the Teaching of Mathematics dept in Teacher's College Columbia.

Philip Lloyd's notes and explanations

PHANTOM GRAPHS - Home1
PHANTOM GRAPHS - Home2

Phantom Graph Witch of Agnesi

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