The Leibniz sequence is the most simple way to describe the equivalence class under multiplication by non-zero rationals of numbers that contains both pi and tau:
1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ...
which sums to equivalently pi/4 or tau/8.
The fundamental simplicity of the Leibniz sequence makes this value the only natural choice from that equivalence class. Let us call it lambda, for Leibniz.
Then the area of the unit circle is 4 lambda, the diameter of the unit circle is 8 lambda, the volume of the unit sphere is 16 lambda, the surface of the unit sphere is 16/3 lambda, etc.
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