The Pythagorean Theorem - Educational Outreach

The commonly accepted value is about 21degree, obtainedby holding out your thumb and, by doing so, barely0covering the lunar disk. Taking exactly half of 0.5tocomplete one very huge right triangle, we obtainRmoon0 tan(0.25 ) 240,002.5milesR 1047milesDmoonmoon 2Rmoon 2094milesThe calculated diameter 2094 miles is 66 miles shy of thetrue value. To illustrate the angular sensitivity associatedwith these results, suppose more sophisticatedinstrumentation indicates that the sweep angle between the0two lunar limbs is actually 0 .515 , an increase of 3 % .Revising the previous givesRmoon0 tan(0.2575 ) 240,002.5milesR 1078.63milesDmoonmoon 2157.26milesnow only a couple of miles shy of the true value. Whendealing with tiny angles, precision instrumentation is thekey to accurate results. However, the underlyingPythagorean infrastructure is still the same four millenniaafter its inception!---We will now use the distance to the moon to obtainthe distance to the sun. Like a series of celestial steppingstones,one inaccessible distance leads to a secondinaccessible distance, each succeeding distance moreextreme than the previous one.152