mathemachristian [he/him]

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Joined 3 years ago
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Cake day: September 15th, 2023

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  • phoenix-sweat It is πr2 or, equivalently, 1/2 τr2

    phoenix-think But wait since π is defined in terms of the diameter it should be 1/4 πD2 .

    phoenix-evidence In fact look at all these quadratic forms

    • distance fallen in a gravitational field: 1/2 gt2
    • energy of motion: 1/2 mv2
    • speed 1/2 at2
    • area of a circle 1/2 τr2

    phoenix-objection-1phoenix-objection-2 Because when you step up from the linear, one dimensional circumference, and integrate, then the antiderivative should have a 1/2 factor to account for the square when differentiating back. The fact that π cancels this factor, and hides it is to its detriment!

    phoenix-smug Read https://www.tauday.com/tau-manifesto again, specifically section 3. τ is how the circumference of a unit circle should be defined since we use the radius and never the diameter. Anything else is revisionism comrade, do better.