Category Archives: Mathematics

Rhetological fallacies

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Appeal to Anonymous Authority

Using evidence from an unnamed 'expert', 'study' or generalized group (like 'scientists') to claim something is true.

“They say that it takes 7 years to digest chewing gum.”

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Floating-point tolerance tests

Absolute tolerance:

  • Not good for big numbers
abs(x–y) <= tol1

Relative tolerance:

  • Not good for small numbers
abs(x–y) <= tol2 * max(abs(x), abs(y))

Combined tolerance test:

(abs(x-y) <= tol1) ||
  (abs(x-y) <= tol2 * max(abs(x), abs(y))

equal to:

abs(x-y) <= tol1 * Max(1.0f, tol2/tol1 * max(abs(x), abs(y))

which for tol1=tol2 becomes:

abs(x-y) <= tol1 * Max(1.0f, abs(x), abs(y))



  • Real time collision detection, Christer Ericson