re-init

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+
+### pi.awk, https://en.wikipedia.org/wiki/Pi
+# In 1706 John Machin used the Gregory–Leibniz series to produce an algorithm
+# that converged much faster. Machin reached 100 digits of π with this
+# formula. Other mathematicians created variants, now known as Machin-like
+# formulae, that were used to set several successive records for calculating
+# digits of π. Machin-like formulae remained the best-known method for
+# calculating π well into the age of computers, and were used to set records
+# for 250 years, culminating in a 620-digit approximation in 1946 by Daniel
+# Ferguson–the best approximation achieved without the aid of a calculating
+# device.
+
+function pi() {
+    return 4*(4*atan2(1,5) - atan2(1,239))
+}
+
+BEGIN {
+    if (ARGV[1] > 0)
+        fig = ARGV[1]
+    else
+        fig = 6
+    str = "%." fig "g\n"
+    printf(str, pi())
+}