Generalized superparticulars - Revision history

Fredg999: Merged within Superparticular ratio

2023-02-25T22:59:54Z

← Older revision		Revision as of 22:59, 25 February 2023
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	~~According to Thomas Taylor's~~ [https://books.google.com.au/books?id=VuY3AAAAMAAJ Theoretic Arithmetic, in Three Books], superparticular ratios are defined as those for which the denominator divides into the numerator once, leaving a remainder of one.		#REDIRECT [[Superparticular ratio#Generalizations]]

	In almost every case, this checks out with the popular usage of superparticular to mean ratios of the form (n+1)/n. In only one case does it deviate: that of 2/1. According to Taylor, 2/1 is not superparticular, because 1 divides into 2 twice, leaving a remainder of 0.

	~~Taylor's book further describes generalizations of the superparticulars:~~
	* superbiparticulars are those where the denominator divides into the numerator once, but leaves a remainder of two (such as 5/3)
	* double superparticulars are those where the denominator divides into the numerator twice, leaving a remainder of one (such as 5/2)
	* one can go on and on, with e.g. triple supertriparticulars where both the divisions and the remainder are 3 (such as 15/4).

	~~More details can be found on this forum thread here:~~ [~~http://forum.sagittal.org/viewtopic.php?f=4&t=410 Generalisation of the terms "epimoric" and "superparticular" as applied to ratios]~~

	~~[[Category:Terms]]~~
	~~[[Category:Math~~]]

Cmloegcmluin: add categories

2021-12-10T17:29:15Z

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← Older revision		Revision as of 17:29, 10 December 2021
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	More details can be found on this forum thread here: [http://forum.sagittal.org/viewtopic.php?f=4&t=410 Generalisation of the terms "epimoric" and "superparticular" as applied to ratios]		More details can be found on this forum thread here: [http://forum.sagittal.org/viewtopic.php?f=4&t=410 Generalisation of the terms "epimoric" and "superparticular" as applied to ratios]

			[[Category:Terms]]
			[[Category:Math]]

Cmloegcmluin: Created page with "According to Thomas Taylor's [https://books.google.com.au/books?id=VuY3AAAAMAAJ Theoretic Arithmetic, in Three Books], superparticular ratios are defined as those for which th..."

2020-02-24T07:52:48Z

Created page with "According to Thomas Taylor's [https://books.google.com.au/books?id=VuY3AAAAMAAJ Theoretic Arithmetic, in Three Books], superparticular ratios are defined as those for which th..."

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According to Thomas Taylor's [https://books.google.com.au/books?id=VuY3AAAAMAAJ Theoretic Arithmetic, in Three Books], superparticular ratios are defined as those for which the denominator divides into the numerator once, leaving a remainder of one.

In almost every case, this checks out with the popular usage of superparticular to mean ratios of the form (n+1)/n. In only one case does it deviate: that of 2/1. According to Taylor, 2/1 is not superparticular, because 1 divides into 2 twice, leaving a remainder of 0.

Taylor's book further describes generalizations of the superparticulars:
* superbiparticulars are those where the denominator divides into the numerator once, but leaves a remainder of two (such as 5/3)
* double superparticulars are those where the denominator divides into the numerator twice, leaving a remainder of one (such as 5/2)
* one can go on and on, with e.g. triple supertriparticulars where both the divisions and the remainder are 3 (such as 15/4).

More details can be found on this forum thread here: [http://forum.sagittal.org/viewtopic.php?f=4&t=410 Generalisation of the terms "epimoric" and "superparticular" as applied to ratios]