File:0.999... = 1 CircleGraphProof.svg
Summary
| Description |
English: A circle of unit area as geometric proof of the equality that 0.999…= 1. Explanation:
A circle of unit area can be sliced up in any way and all of its parts added together will always equal 1. This circle is sliced up into ever-thinner pie slices where the first slice leaves 90% untouched (0.9), the second slice leaves 90% of the remaining wedge untouched (0.09), the third slice leaves 90% of that remaining wedge untouched (0.009), and this process continues without end. The summation of all slices produces the infinite series: diagramBlue = RGBColor[0.4, 0.8, 1];
coord[n_Integer] := {
Cos[(1/4 + 10^(-n)) 2 \[Pi]],
Sin[(1/4 + 10^(-n)) 2 \[Pi]]
}
radius[n_Integer] := Line[{{0, 0}, coord[n]}]
pointLabel[label_String, points_List : {x_, y_}] := Text[
TextCell[
label,
"Text",
CellFrame -> True,
CellFrameMargins -> 0.1,
CellFrameColor -> diagramBlue,
Background -> White
],
points
]
diagram = Show[
Graphics[{
{diagramBlue, EdgeForm[Black], Disk[]},
radius[0],
radius[1],
radius[2],
radius[3],
pointLabel["0.9\n36°", coord[1] + {-0.05, 0.11}],
pointLabel[
"0.09\n3.6°", {coord[2][[1]] - 0.05, coord[0][[2]] + 0.12}],
pointLabel[
"0.009\n0.36°", {coord[3][[1]] + 0.05, coord[0][[2]] + 0.12}]
}],
ImageSize -> 500
]
Export[FileNameJoin[{Directory[], "Downloads",
"0.999... = 1 CircleGraphProof.svg"}], diagram]
|
| Date | |
| Source | Own work based on: 0.999... = 1 CircleGraphProof.png |
| Author | CalendulaAsteraceae |
| SVG development |
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