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NEW DISCOVERY (October 3, 2023): The Geometric Mean of x and y is the midpoint of the tangent slope of radii (adjacent/tangent circles) x and y.

The Geometric Mean of two numbers x and y is given as the square root of (x*y) = GM = (x*y)^.5.

Swipe photos for the Geometric Proof.

We (RG and Talal Ghannam PhD) will be publishing this paper that includes several other novel and related geometric discoveries (and their respective proofs) very soon.

While other mathematicians (including John Wallace, circa 1616) have identified other tangent relationships to GM values, this particular relationship appears to be a novel discovery as it is (so far) absent from the academic literature.

PS: Isn’t the Universe incredibly beautiful?! God is truly the Masterpiece Creator and Architect, it reminds me of the quotation : “A bit of science distances one from God, but much science nears one to God.” (Pasteur)