Trigonometry - Revision history

Manidh at 08:34, 9 January 2023

2023-01-09T08:34:25Z

← Older revision		Revision as of 14:04, 9 January 2023
Line 56:		Line 56:
	== References ==		== References ==
	<references />		<references />

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Organic Articles English]]		[[Category:Organic Articles English]]
	~~[[Category:Vigyan Ready]]~~

Indicwiki: 15 revisions imported from :alpha:Trigonometry

2023-01-09T08:26:36Z

15 revisions imported from alpha:Trigonometry

← Older revision	Revision as of 13:56, 9 January 2023
(No difference)

alpha>Ramamurthy S: Category added

2023-01-09T05:52:17Z

Category added

← Older revision		Revision as of 11:22, 9 January 2023
Line 58:		Line 58:
	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Organic Articles English]]		[[Category:Organic Articles English]]
			[[Category:Vigyan Ready]]

alpha>Ramamurthy S: category added

2023-01-02T13:55:47Z

category added

← Older revision		Revision as of 19:25, 2 January 2023
Line 57:		Line 57:
	<references />		<references />
	[[Category:Mathematics]]		[[Category:Mathematics]]
			[[Category:Organic Articles English]]

alpha>Ramamurthy S: Category added

2023-01-02T13:33:01Z

Category added

← Older revision		Revision as of 19:03, 2 January 2023
Line 55:		Line 55:

	== References ==		== References ==
			<references />
			[[Category:Mathematics]]

alpha>Ramamurthy S: /* Jyā */

2023-01-02T13:23:53Z

Jyā

← Older revision		Revision as of 18:53, 2 January 2023
Line 1:		Line 1:
	Hindu name for the science of Trigonometry is ''Jyotpatti-ganita'' or "the science of calculation for the construction of the sine"<ref>{{Cite book\|last=Narayan Singh\|first=Avadhesh\|title=Hindu Trigonometry\|last2=Datta\|first2=Bibhutibhusan}}</ref>. It is found as early as in the ''Brāhma-sphuṭa-siddhānta'' of [[Brahmagupta]] (628). In the recent years name appeared as ''Trikoṇamiti''.		Hindu name for the science of Trigonometry is ''Jyotpatti-ganita'' or "the science of calculation for the construction of the sine"<ref>{{Cite book\|last=Narayan Singh\|first=Avadhesh\|title=Hindu Trigonometry\|last2=Datta\|first2=Bibhutibhusan}}</ref>. It is found as early as in the ''[[Brāhma-sphuṭa-siddhānta]]'' of [[Brahmagupta]] (628). In the recent years name appeared as ''Trikoṇamiti''.
	[[File:Trigonometry.jpg\|alt=Fig.1\|thumb\|Fig.1]]		[[File:Trigonometry.jpg\|alt=Fig.1\|thumb\|Fig.1]]
	The Hindus introduced and employed three trigonometrical functions namely ''jyā , koṭi-jyā , utkrama-jyā''. They are functions of an arc of a circle, but not of an angle. If AP is an arc of a circle with centre at O, then its ''jyā''=PM, ''koṭi-jyā''=OM and ''utkrama-jyā''=OA-OM =AM. Hence their relation with modern trigonometrical functions will be		The Hindus introduced and employed three trigonometrical functions namely ''jyā , koṭi-jyā , utkrama-jyā''. They are functions of an arc of a circle, but not of an angle. If AP is an arc of a circle with centre at O, then its ''jyā''=PM, ''koṭi-jyā''=OM and ''utkrama-jyā''=OA-OM =AM. Hence their relation with modern trigonometrical functions will be
Line 10:		Line 10:
	are ''jīvā'', ''śiñjinī'' , ''guṇa'' , ''maurvī'' etc. This trigonometrical function is also called ''ardha-jyā'' (“half-chord") or ''jyārdha'' ("chord-half"). Thus Bhaskara II (1150) explicitly observes, "It should be known that ''ardha-jyā'' is here called "''jyā''".		are ''jīvā'', ''śiñjinī'' , ''guṇa'' , ''maurvī'' etc. This trigonometrical function is also called ''ardha-jyā'' (“half-chord") or ''jyārdha'' ("chord-half"). Thus Bhaskara II (1150) explicitly observes, "It should be known that ''ardha-jyā'' is here called "''jyā''".

	Parameśvara (1430) remarks:		[[Parameśvara]] (1430) remarks:

	"A part of a circle is of the form of a bow, so it is called the "bow" (dhanu). The straight line joining its two extremities is the "bow-string" (''jīvā''); it is really the "full-chord” (samasta-jyā). Half of it is here (called) the "half-chord" (''ardha-jyā''), and half that arc is called the "bow" of that half-chord. In fact the Rsine (''jyā'') and Rcosine (''koṭi-jyā'') of that bow are always half-chords."		"A part of a circle is of the form of a bow, so it is called the "bow" (dhanu). The straight line joining its two extremities is the "bow-string" (''jīvā''); it is really the "full-chord” (samasta-jyā). Half of it is here (called) the "half-chord" (''ardha-jyā''), and half that arc is called the "bow" of that half-chord. In fact the Rsine (''jyā'') and Rcosine (''koṭi-jyā'') of that bow are always half-chords."
Line 43:		Line 43:
	s=h tan z, d=h sec z.		s=h tan z, d=h sec z.

	Similar rules occur in other astronomical works also. In the Gaṇita-sāra-saṅgraha of Mahāvīra (850) by the term "shadow” of a gnomon is sometimes meant the ratio of the actual shadow to the height of the gnomon. This ratio, as has been just stated, is equal to the tangent of the zenith distance of the sun.		Similar rules occur in other astronomical works also. In the [[Gaṇita-sāra-saṅgraha]] of [[Mahāvīra]] (850) by the term "shadow” of a gnomon is sometimes meant the ratio of the actual shadow to the height of the gnomon. This ratio, as has been just stated, is equal to the tangent of the zenith distance of the sun.

	== See Also ==		== See Also ==

alpha>Ramamurthy S: /* External Links */

2023-01-02T13:10:42Z

External Links

← Older revision		Revision as of 18:40, 2 January 2023
Line 51:		Line 51:

	* [[:en:Jyā,_koti-jyā_and_utkrama-jyā\|Hindu Trigonometry]]		* [[:en:Jyā,_koti-jyā_and_utkrama-jyā\|Hindu Trigonometry]]
			*[https://www.myindiamyglory.com/2019/05/09/the-evolution-of-algebra-trigonometry-and-calculus-in-ancient-india/ Evolution of trigonometry in ancient India/]
	*		*

	== References ==		== References ==

alpha>Ramamurthy S: /* External Links */

2023-01-02T13:08:25Z

External Links

← Older revision		Revision as of 18:38, 2 January 2023
Line 49:		Line 49:

	== External Links ==		== External Links ==

			* [[:en:Jyā,_koti-jyā_and_utkrama-jyā\|Hindu Trigonometry]]
			*

	== References ==		== References ==

alpha>Ramamurthy S: /* See Also */

2023-01-02T07:01:53Z

See Also

← Older revision		Revision as of 12:31, 2 January 2023
Line 1:		Line 1:
	Hindu name for the science of Trigonometry is ''Jyotpatti-ganita'' or "the science of calculation for the construction of the sine". It is found as early as in the ''Brāhma-sphuṭa-siddhānta'' of [[Brahmagupta]] (628). In the recent years name appeared as ''Trikoṇamiti''.		Hindu name for the science of Trigonometry is ''Jyotpatti-ganita'' or "the science of calculation for the construction of the sine"<ref>{{Cite book\|last=Narayan Singh\|first=Avadhesh\|title=Hindu Trigonometry\|last2=Datta\|first2=Bibhutibhusan}}</ref>. It is found as early as in the ''Brāhma-sphuṭa-siddhānta'' of [[Brahmagupta]] (628). In the recent years name appeared as ''Trikoṇamiti''.
	[[File:Trigonometry.jpg\|alt=Fig.1\|thumb\|Fig.1]]		[[File:Trigonometry.jpg\|alt=Fig.1\|thumb\|Fig.1]]
	The Hindus introduced and employed three trigonometrical functions namely ''jyā , koṭi-jyā , utkrama-jyā''. They are functions of an arc of a circle, but not of an angle. If AP is an arc of a circle with centre at O, then its ''jyā''=PM, ''koṭi-jyā''=OM and ''utkrama-jyā''=OA-OM =AM. Hence their relation with modern trigonometrical functions will be		The Hindus introduced and employed three trigonometrical functions namely ''jyā , koṭi-jyā , utkrama-jyā''. They are functions of an arc of a circle, but not of an angle. If AP is an arc of a circle with centre at O, then its ''jyā''=PM, ''koṭi-jyā''=OM and ''utkrama-jyā''=OA-OM =AM. Hence their relation with modern trigonometrical functions will be
Line 46:		Line 46:

	== See Also ==		== See Also ==
			[[त्रिकोणमिति-हिन्दू]]

	== External Links ==		== External Links ==

	== References ==		== References ==

alpha>Ramamurthy S at 06:56, 2 January 2023

2023-01-02T06:56:21Z

← Older revision		Revision as of 12:26, 2 January 2023
Line 44:		Line 44:

	Similar rules occur in other astronomical works also. In the Gaṇita-sāra-saṅgraha of Mahāvīra (850) by the term "shadow” of a gnomon is sometimes meant the ratio of the actual shadow to the height of the gnomon. This ratio, as has been just stated, is equal to the tangent of the zenith distance of the sun.		Similar rules occur in other astronomical works also. In the Gaṇita-sāra-saṅgraha of Mahāvīra (850) by the term "shadow” of a gnomon is sometimes meant the ratio of the actual shadow to the height of the gnomon. This ratio, as has been just stated, is equal to the tangent of the zenith distance of the sun.

			== See Also ==

			== External Links ==

			== References ==