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Summary

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English: A circle of unit area as geometric proof of the equality that 0.999...= 1.

Explanation: A circle of unit area can be slice up in any way and all of those 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:

0.9 + 0.09 + 0.009 + 0.0009 + ... = 0.9999...

And because the slicing never changes the total area of this circle with an area of 1 (both prior to the slicing and after), the conclusion is that:

0.9999... = 1.
Date
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Author Tdadamemd
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Date/TimeThumbnailDimensionsUserComment
current06:04, 24 January 2013Thumbnail for version as of 06:04, 24 January 2013800 × 800 (22 KB)AnonMooscrop
04:27, 24 January 2013Thumbnail for version as of 04:27, 24 January 20131,000 × 1,000 (36 KB)TdadamemdFixing degree symbols.
20:43, 23 January 2013Thumbnail for version as of 20:43, 23 January 20131,000 × 1,000 (54 KB)TdadamemdUser created page with UploadWizard

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