True Value of Pi

  # True Value of Pi
  mathematics golden pi geometry

🔬 Live graph · Laws of appearance

The Kepler-triangle closure with the constant left free: the site's own R, S and their difference, computed live. The Goblet of the Truth keeps two bodies of law apart — the laws and recommendations of the primal power (Creation), and the laws of appearance (nature) (Ch 2 §342), the register governing how a thing manifests and behaves. Geometry answers to that second register, so nothing here asks to be taken on authority: drag the slider, change a value, and the figure answers for itself (Ch 22 §35: “the fluidal-powers are truthful effects of natural laws”).

  The conventional value of π = 3.14159... is the *approximate* ratio used in engineering. **Golden Pi** proposes that the *true* geometric value is:

  π = 4 / √Φ = 3.144605511029693...

  ## Comparison
  | Constant | Value |

| --- | --- | | Φ (Golden Ratio) | 1.618033988749895... | | √Φ | 1.272019649514069... | | Golden Pi (4/√Φ) | 3.144605511029693... | | Conventional π | 3.141592653589793... |

  ## Derivation
  From [Kepler's Right Triangle](kepler-triangle.html), where the sides are in the ratio **1 : √Φ : Φ**, the triangle's full base — when the triangle is scaled so that the hypotenuse is 2√Φ and the height is 2 — is exactly 4/√Φ, the same length as Golden Pi.


    **See also:**
    [Kepler's Right Triangle](kepler-triangle.html) ·
    [Squaring the Circle](squaring-the-circle.html) ·
    [Golden Ratio (Φ)](phi.html) ·
    [Pyramid of Giza](pyramid-of-giza.html)