[math-fun] Cool Heron's Formula example

From John L. Gustafson's discussion with Kahan re floating point:

Triangle with side lengths a,b,c. a=b=7/2+3*2^(-111), c=7 Units are light-years. Note that 3*2^(-111) is ~1/200 size of a proton. Area ~ 55x Earth's surface. Believe it or not, the triangle altitude is ~ 85 cm ~ 33.5" -- almost a yard. Don't try this calculation at home; it's Herondisly inaccurate.