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A beautiful constant (the MRB constant)

Compare the results of these two sets of code. The first one is based on the MRB constant (0.18785...), and the second one, 1/e (0.367879...). Can you change these 3 trig formulas so that 1/e (or any other constant) gives the same appearance as the MRB constant does? Or are these graphs from these 3 families of trig formulas unique to the MRB constant?

m = 0.1878596424620671202485179340542732300559030949001387861720046840\
89477231564660213703296654433107496903
ListPlot[Table[Sin[Pi/m*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[Cos[Pi/m*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[
  Tan[Pi/m*(5060936308 + 78389363/24*n)], {n, -100, 100}], 
 Joined -> True]

enter image description hereenter image description hereenter image description here

d = 1/E
ListPlot[Table[Sin[Pi/d*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[Cos[Pi/d*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[
  Tan[Pi/d*(5060936308 + 78389363/24*n)], {n, -100, 100}], 
 Joined -> True]

enter image description hereenter image description hereenter image description here

P.S. It doesn't take much to simply get "geometric" shapes out of this family of trig formulas. Try the following code:

d = 1/E - 10^-2
ListPlot[Table[Sin[Pi/d*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[Cos[Pi/d*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[
  Tan[Pi/d*(5060936308 + 78389363/24*n)], {n, -100, 100}], 
 Joined -> True]

enter image description here

Plus, it don't take much error in the MRB constant's approximate value to really disfigure it's graphs. Try this code where you only use 12 digits of precision :for the MRB constant

m = 0.187859642462
ListPlot[Table[Sin[Pi/m*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[Cos[Pi/m*(5060936308 + 78389363/24*n)], {n, -100, 100}]]
ListPlot[Table[
  Tan[Pi/m*(5060936308 + 78389363/24*n)], {n, -100, 100}], 
 Joined -> True]

enter image description here

POSTED BY: Marvin Ray Burns
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