Category Archives: Mathematics

Rhetological fallacies

Copy from  here

 

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))

 

References:

  • Real time collision detection, Christer Ericson