A lay person might think that it would be satisfying enough to know the number to half a dozen places of decimals. No: mathematicians want to know it exactly, if they can. Not just because they are weird obsessives, but because they know from experience that getting that exact value often opens unexpected doors and throws light on the underlying math. The mathematical term of art for this exact representation of a number is “closed form.” A mere decimal approximation, however good, is an “open form.” The number 1.6449340668… is an open form.
