Pythagorean Ratios in Art and Music

After reviewing squares, square roots and rational and irrational numbers, students learn about the Pythagorean philosophy of harmony and balance in all things. Balance is further explored through the construction of mobiles.

Mathematical Concepts

  • Rational and irrational numbers
  • Direct and inverse proportions
  • Fractions, decimals, percents, ratios


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Some Pythagorean Beliefs: 

Only ten colors exist – white, black, yellow, tawny (a mustard color), pale (off-white), red, green, blue, light blue, and gray. Dancing should be “accompanied by a lyre because the pipe is too theatrical and leads to insolence.” Proper music, a vegetarian diet and exercise, playing the monochord, making geometric constructions, and studying abstract mathematics lead to harmony of body and psyche.