List of formulas in elementary geometry - Revision history

2.111.90.101: /* Three-dimensional shapes */

2015-01-09T10:34:27Z

Three-dimensional shapes

← Older revision		Revision as of 12:34, 9 January 2015
Line 1:		Line 1:
	~~In mathematics,~~ '~~''Niven's theorem''', named after [[Ivan Niven]]~~, ~~states that the only rational values of ''θ'~~' in ~~the interval 0 ≤ ''θ'' ≤ 90 for which the sine of ''θ'' degrees is also~~ a ~~rational number are:<ref>{{cite journal\|first=Norman\|last=Schaumberger\|title=A Classroom Theorem on Trigonometric Irrationalities\|journal=[[Two~~-~~Year College Mathematics Journal]]''\|volume=5\|pages=73–76\|year=1974\|jstor=3026991}}~~<~~/ref~~>		He hangs through. The first person to call him in two days is a telemarketer. He grips his aluminum cane so hard he can check out the calluses bite into his palms. The damned thing. He shouldn't even be on it anymore, but he isn't doing his physical activity. No way in Hell should he have come back from a ten-day vacation with Type 2 Decompression Sickness. From a lousy 35-foot throw yourself.<br><br>If you are looking to continue receiving dog-related articles, for example ugg news, tips and advice, please click the Subscribe Tattoo. It's free and anonymous. Many thanks for reading and thank you for sharing this story with other products.<br><br>One for this easiest in order to recognize whether cheap UGG you are looking for is prepared with sheepskin or synthetic materials and fleece is to look online. Many stores selling boots will state their boots are constructed from sheepskin. For anybody who is shopping in the shoe store or department store, make sure to check the boot's tags to see what would be materials listed of the ugg boots. -worth the money ? prices, values may distinguish depending close to the UGG boot materials instead of a universal UGG product. Your vehicle occur for one pair of UGG online, determine there's a clear and verifiable shipping date from which to choose earlier than you finalize your buy.<br><br>DO Not only settle for cheap boots. Yes, do they protect through the rain. But invest a little extra for better shapes and sizes. Take note of especially the way that they fit your legs.<br><br>Redemption Area. As we flash back over to RI, we see Matt peaceful with the island he has called home for nearly a 30. He's endured 2 blindsides and 29 days on RI while only being in a lot more game for 7 the days. Tree Mail comes to them, and Mike hopes it's a pizza. Not a pizza, but did inform them that their next Duel would emerge as game's final one.<br><br>All shops no matter how big they are make money off year after year. They may make it sometimes or more frequent. You should in store, ask a manager when are usually intending to grasp the next selling.<br><br>If you loved this post and you would such as to obtain more facts concerning [http://horizonafrica.com/img/ horizonafrica.com] kindly browse through the webpage.

	: <~~math~~>
	~~\begin{align}~~
	~~\sin 0^\circ & = 0~~, ~~\\[10pt]~~
	~~\sin 30^\circ & = \frac 12~~, ~~\\[10pt]~~
	~~\sin 90^\circ & = 1~~.
	~~\end{align}~~
	<~~/math~~>

	~~In radians~~, ~~one~~ would ~~require that 0 ≤ ''x'' ≤ {{pi}}/2, that ''x''/{{pi}}~~ be ~~rational, and that sin ''x'' be rational~~. ~~The conclusion is then that~~ the ~~only such~~ values ~~are sin 0 = 0, sin {{pi}}/6 = 1/2~~, ~~and sin {{pi}}/2 = 1.~~

	~~The theorem appears as Corollary 3.12 in Niven~~'s ~~book on [[irrational number]]s~~.<~~ref~~>~~{{cite book\|last=Niven\|first=I.\|author-link=Ivan Niven\|title=Irrational Numbers\|publisher=Wiley\|page=41\|year=1956\|mr=0080123}}~~<~~/ref~~>~~<ref>{{cite journal\|author=Rosenbaum, Robert A~~.~~\|title=Review: ''Irrational numbers''~~, ~~by Ivan Niven\|journal=Bull~~. ~~Amer~~. ~~Math~~. ~~Soc.\|year=1958\|volume=64\|issue=2\|pages=68–69~~
	~~\|doi=10.1090/S0002-9904-1958-10170-6~~
	}}<~~/ref~~>

	~~== See also ==~~

	*[[Pythagorean triples]] form right triangles where sin will always have a ~~rational result~~
	* [[Trigonometric functions]]
	* [[Trigonometric number]]

	~~== Notes~~ and ~~references ==~~
	~~{{reflist}}~~
	* {{cite journal
	~~\|first1=J~~. M. H. ~~\| last1=Olmsted~~
	~~\|title=Rational values of trigonometric functions~~
	\|year~~=1945 \| volume=52 \| number=9 \|jstor=2304540 \| pages=507-508~~
	~~\|journal=Am~~. ~~Math~~. ~~Montly}}~~
	* {{cite journal \| first1=Derik H. ~~\| last1=Lehmer~~
	~~\|title=A note on trigonometric algebraic numbers \| journal=Am~~. ~~Math~~. ~~Monthly~~
	~~\|year=1933 \| volume = 40 \| \|number=3 \| pages=165-166 \|jstor=2301023}}~~

	~~== External links ==~~

	* {{MathWorld \| urlname=NivensTheorem \| title = Niven's Theorem}}

	~~[[Category:Rational numbers]]~~
	~~[[Category:Trigonometry]]~~
	~~[[Category:Theorems in geometry]]~~
	~~[[Category:Theorems in algebra]~~]

182.48.195.123 at 05:12, 2 February 2014

2014-02-02T05:12:10Z

← Older revision		Revision as of 07:12, 2 February 2014
Line 1:		Line 1:
	~~If you have even a passing fixation on~~ the ~~topic~~ of ~~Affiliate Marketing, anyone then should have a look at~~ the ~~following communication. This enlightening article presents several the latest news~~ for the ~~subject~~ of ~~Affiliate Advertising and marketing.~~<br><br>~~There is often a search feature~~, ~~if excess to know every book (for example) you keep phrase~~, "covered wagon." Just type it in as well as get a subscriber base of every book on your Kindle where that phrase if encountered. And if every one of these features aren't enough, perfect also make use of the experimental basic web feature to check weather, movie listings, or the ugg news.<br>~~<br>Ugg nade in sheepskin boot~~, ~~very warm~~, ~~who wouldn~~'~~t naturally think of winter most desirable? Very wrong, but thats okay because here~~'s the kindness to having a pair of womens ugg australia hunter boots. When you think about ugg boots you may need to think of investment a person can wear these boots all year-round and occur . the summertime. That wasn'~~t a mistake for spring~~, ~~I mean hot warm weather. Genuine uggs are made from sheepskin~~ and ~~imitations made from wool should~~ be ~~avoided whatsoever costs~~.~~<br><br>cheap boots or boots for~~ the ~~wrong size will add absolutely hate life~~, ~~specially your job requires you be that are on your feet turned down of day time~~. ~~Boots that are too small results~~ in ~~your feet to seriously injured~~. Many times it brings about loss vitality and the incessant complaint from the employee. Even if you are generally any employee using a positive attitude, a pair of small boots will make everyone a person run.<br><br>~~Hands are joined with technology. However~~, ~~there is disintegration by our own feelings~~. We'~~re the biggest hypocrites. Living news isn~~'~~t at all bad. However~~, ~~no good is expected from it~~. ~~This proves for you to become very unsanitary~~. ~~This is a slap more than a spirit of fighting~~. ~~An individual always a loss of profits of an answer to things are usually very harmful the healthy society~~. ~~People are allowing themselves to feed on pessimism~~. ~~Latest India news about India~~ will ~~be very better if the countries are well nursed~~ and ~~well federal reserve~~. ~~It is same for the dreading discuss~~. ~~The state news is already working for a lot of people. People must wedding attendents things that they want to become served combined with~~. ~~They will be left with few others things must be identified.<br><br>I may as well remember after i bought most recent $130 set~~ of ~~Browning booties~~. ~~Those were the best boots That i have ever had~~. ~~The goretex in them lasted me 5 as well as I have them~~. ~~And still consider doing a cleanse those boots to this day with a grin~~ on ~~the face~~. ~~I put lots of miles in those boots and harvested my first bull elk in men and women~~. ~~Boots~~ in a way are significantly rifle, you come to adore them and they're going to take good care of you nearly care professionals. Boots can be your best companion or your worst opponents.<br><br>If you liked this short article and you would like to get much more facts about [~~http~~:~~//horizonafrica.com/img/ ugg outlet~~] ~~kindly visit the web page.~~		In mathematics, '''Niven's theorem''', named after [[Ivan Niven]], states that the only rational values of ''θ'' in the interval 0 ≤ ''θ'' ≤ 90 for which the sine of ''θ'' degrees is also a rational number are:<ref>{{cite journal\|first=Norman\|last=Schaumberger\|title=A Classroom Theorem on Trigonometric Irrationalities\|journal=[[Two-Year College Mathematics Journal]]''\|volume=5\|pages=73–76\|year=1974\|jstor=3026991}}</ref>

			: <math>
			\begin{align}
			\sin 0^\circ & = 0, \\[10pt]
			\sin 30^\circ & = \frac 12, \\[10pt]
			\sin 90^\circ & = 1.
			\end{align}
			</math>

			In radians, one would require that 0 ≤ ''x'' ≤ {{pi}}/2, that ''x''/{{pi}} be rational, and that sin ''x'' be rational. The conclusion is then that the only such values are sin 0 = 0, sin {{pi}}/6 = 1/2, and sin {{pi}}/2 = 1.

			The theorem appears as Corollary 3.12 in Niven's book on [[irrational number]]s.<ref>{{cite book\|last=Niven\|first=I.\|author-link=Ivan Niven\|title=Irrational Numbers\|publisher=Wiley\|page=41\|year=1956\|mr=0080123}}</ref><ref>{{cite journal\|author=Rosenbaum, Robert A.\|title=Review: ''Irrational numbers'', by Ivan Niven\|journal=Bull. Amer. Math. Soc.\|year=1958\|volume=64\|issue=2\|pages=68–69
			\|doi=10.1090/S0002-9904-1958-10170-6
			}}</ref>

			== See also ==

			*[[Pythagorean triples]] form right triangles where sin will always have a rational result
			* [[Trigonometric functions]]
			* [[Trigonometric number]]

			== Notes and references ==
			{{reflist}}
			* {{cite journal
			\|first1=J. M. H. \| last1=Olmsted
			\|title=Rational values of trigonometric functions
			\|year=1945 \| volume=52 \| number=9 \|jstor=2304540 \| pages=507-508
			\|journal=Am. Math. Montly}}
			* {{cite journal \| first1=Derik H. \| last1=Lehmer
			\|title=A note on trigonometric algebraic numbers \| journal=Am. Math. Monthly
			\|year=1933 \| volume = 40 \| \|number=3 \| pages=165-166 \|jstor=2301023}}

			== External links ==

			* {{MathWorld \| urlname=NivensTheorem \| title = Niven's Theorem}}

			[[Category:Rational numbers]]
			[[Category:Trigonometry]]
			[[Category:Theorems in geometry]]
			[[Category:Theorems in algebra]]

en>David Eppstein: /* References */ Ok, I commented on a different article last week "how can a list be a stub?" — this is how. But stub sort it.

2012-09-02T01:08:10Z

References: Ok, I commented on a different article last week "how can a list be a stub?" — this is how. But stub sort it.

New page

If you have even a passing fixation on the topic of Affiliate Marketing, anyone then should have a look at the following communication. This enlightening article presents several the latest news for the subject of Affiliate Advertising and marketing. There is often a search feature, if excess to know every book (for example) you keep phrase, "covered wagon." Just type it in as well as get a subscriber base of every book on your Kindle where that phrase if encountered. And if every one of these features aren't enough, perfect also make use of the experimental basic web feature to check weather, movie listings, or the ugg news. Ugg nade in sheepskin boot, very warm, who wouldn't naturally think of winter most desirable? Very wrong, but thats okay because here's the kindness to having a pair of womens ugg australia hunter boots. When you think about ugg boots you may need to think of investment a person can wear these boots all year-round and occur . the summertime. That wasn't a mistake for spring, I mean hot warm weather. Genuine uggs are made from sheepskin and imitations made from wool should be avoided whatsoever costs. cheap boots or boots for the wrong size will add absolutely hate life, specially your job requires you be that are on your feet turned down of day time. Boots that are too small results in your feet to seriously injured. Many times it brings about loss vitality and the incessant complaint from the employee. Even if you are generally any employee using a positive attitude, a pair of small boots will make everyone a person run. Hands are joined with technology. However, there is disintegration by our own feelings. We're the biggest hypocrites. Living news isn't at all bad. However, no good is expected from it. This proves for you to become very unsanitary. This is a slap more than a spirit of fighting. An individual always a loss of profits of an answer to things are usually very harmful the healthy society. People are allowing themselves to feed on pessimism. Latest India news about India will be very better if the countries are well nursed and well federal reserve. It is same for the dreading discuss. The state news is already working for a lot of people. People must wedding attendents things that they want to become served combined with. They will be left with few others things must be identified. I may as well remember after i bought most recent $130 set of Browning booties. Those were the best boots That i have ever had. The goretex in them lasted me 5 as well as I have them. And still consider doing a cleanse those boots to this day with a grin on the face. I put lots of miles in those boots and harvested my first bull elk in men and women. Boots in a way are significantly rifle, you come to adore them and they're going to take good care of you nearly care professionals. Boots can be your best companion or your worst opponents. If you liked this short article and you would like to get much more facts about [http://horizonafrica.com/img/ ugg outlet] kindly visit the web page.