Pi is the ratio of a circle's circumference to its diameter. It is one of the most important constants in practical mathematics because circles, arcs, wheels, pipes, tanks, gears, pulleys, domes, cylinders, spheres, and rotating parts appear everywhere in measurement and construction.
This folder belongs in A1 because a community can preserve and use pi, e, square-root constants, and common ratios long before it can rebuild advanced mathematics. Small, reliable constants references let teachers, builders, surveyors, machinists, and students calculate circumference, area, volume, curvature, angular relationships, growth factors, logarithmic conversions, and geometric proportions with pencil and paper.
For rough work, 3.14 is often enough. For better workshop and surveying work, 3.1416 or 3.14159 is usually more than enough. NASA/JPL explains that its highest-accuracy interplanetary navigation calculations use 15 decimal places, and that 37 decimal places are enough to calculate the circumference of a circle the size of the observable universe to within the diameter of a hydrogen atom.
For InfoPreserver, a 100-decimal-place reference is a good archival choice. It is far beyond ordinary physical need, but still fits on a readable sheet and protects against copying errors in future derivatives.
The same principle applies to e, square roots, the golden ratio, and degree-radian conversion factors. A few printed constants reduce repeated approximation work and help users check table lookups, slide-rule results, and hand calculations.
Use pi for:
C = pi d or C = 2 pi rA = pi r^2V = pi r^2 hA = 4 pi r^2V = 4/3 pi r^3180 degrees = pi radiansln(10) converts common logarithms into natural logarithmsUsers should keep units attached to every calculation. If the radius is in inches, area is in square inches and volume is in cubic inches.
pi_100_digits_reference.pdf - InfoPreserver one-page reference containing pi to 100 decimal places plus related circle constants.mathematical_constants_reference.pdf - InfoPreserver one-page reference containing pi, e, square-root constants, the golden ratio, logarithmic constants, and degree-radian conversion factors.20_A1_Stabilized_Community/Foundational_Knowledge/Mathematics/Pi_and_Circle_Constants