![\"\"](\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Wandering-Epicycle-Fig2.jpg\")
Here is an intriguing problem from the 2021 Math Calendar.<\/p>\nHere is an intriguing problem from the 2021 Math Calendar.<\/p>\n
\u201cIf the smaller circle of diameter 7 rotates without slipping within the larger circle, what is the length of the path of P?\u201d<\/p>\n
The problem did not state clearly how far the smaller circle should rotate.\u00a0 Its answer implied it should complete just one full (360\u00b0) rotation within the larger circle.<\/p>\n
Recall that all the answers are integer days of the month.<\/p>\n
Answer<\/a>.<\/p>\n See the Wandering Epicycle<\/a> for a solution.<\/p>\n (Update 1\/3\/2022)<\/strong>\u00a0 First, this problem is dealt with in more detail and more expansively on the Mathologer Youtube website by Burkard Polster in his 7 December 2018 post on the \u201cSecrets of the Nothing Grinder<\/a>\u201d (Figure 1).\u00a0 A further, deeper discussion of epicycles is given in the Mathologer\u2019s 6 July 2018 post on \u201cEpicycles, complex Fourier and Homer Simpson’s orbit<\/a>\u201d (Figure 2).\u00a0 And finally, a panoply of related puzzles is given in the 30 December 2021 Mathologer post \u201cThe 3-4-7 miracle. Why is this one not super famous<\/a>\u201d (Figure 3).<\/p>\n This last post reveals the ambiguity of the idea of \u201cone full (360\u00b0) rotation\u201d I disingenuously added to the problem to try to get the answer given in Math Calendar version.<\/p>\n![\"\"](\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Wandering-Epicycle-Answer.jpg\")
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