VISUAL LESSON · 1 PICTURES

Three Mathematical Meanings of Pi

How can the same Greek letter represent different mathematical objects?

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BEFORE THE FIRST PICTURE

How this lesson unfolds.

Begin with Which mathematical world are we in? Use the picture, intuition and explanation together before moving on.

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Which mathematical world are we in?

INTUITION

The circle constant pi, permutation notation such as nPr, and sampling inclusion probability pi_i reuse related symbols but mean different objects; surrounding notation determines the meaning.

  • Learning goalDistinguish the circle constant, permutation notation and first-order inclusion probability from context.
  • Helpful foundationsbasic notation · probability · permutations
  • Common trapA repeated glyph does not force a repeated meaning across different mathematical contexts.
  • Next connectionRead inclusion probabilities in unequal-probability sampling designs