Reciprocal Fibonacci constant - Revision history

en>Cerabot: Dating templates: {{citation needed}} (1). (bot)

2014-12-24T23:09:54Z

Dating templates: {{citation needed}} (1). (bot)

← Older revision		Revision as of 01:09, 25 December 2014
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	~~{{unreferenced\|date=October 2013}}~~		Wilber Berryhill is what his wife loves to call him and he completely loves this name. To climb is some thing I truly appreciate performing. Her family members lives in Ohio but her husband desires them to transfer. Office supervising is where her primary income arrives from.<br><br>My blog - clairvoyants ([http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ alles-herunterladen.de])

	~~[[Image:clockAngles.jpg\|thumb\|The diagram shows the angles formed by the hands of an analog clock showing a time of 2:20]]~~
	~~'''Clock angle problems''' are a type of [[mathematical problem]] which involve finding the angles between the hands of an [[analog clock]].~~

	~~==Math problem==~~
	~~Clock angle problems relate two different measurements: [[angle]]s~~ and ~~[[time]]~~. ~~The angle~~ is ~~typically measured~~ in ~~[[degree (angle)\|degrees]] from the mark of number 12 clockwise~~. ~~The time~~ is ~~usually based on [[12-hour clock]].~~

	A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute.

	~~===Equation for the angle of the hour hand===~~
	~~<math>\theta_{\text{hr}} = \frac{1}{2}M_\Sigma = \frac{1}{2}(60H + M)</math>~~

	where:
	* <math>\scriptstyle\theta</math> is the angle in degrees of the hand measured clockwise from ~~the 12 o'clock position~~.
	* <~~math~~>~~\scriptstyle H~~<~~/math~~> ~~is the hours past 12 o'clock.~~
	* <math>\scriptstyle M</math> is the minutes past the hour.
	* <math>\scriptstyle M_\Sigma</math> is the minutes past 12 o'clock.

	~~===Equation for the angle of the minute hand===~~
	~~<math>\theta_{\text{min.}} = 6M</math>~~

	~~where~~:
	* <math>\scriptstyle\theta</~~math> is the angle in degrees of the hand measured clockwise from the 12 o'clock position.~~
	* <math>\scriptstyle M</~~math> is the minute.~~

	~~====Example====~~
	~~The time is 5:24. The angle in degrees of the hour hand is:~~

	~~<math>\theta_{\text{hr}} = \frac{1}{2}(60 \times 5 + 24) = 162</math>~~

	~~The angle in degrees of the minute hand is:~~

	~~<math>\theta_{\text{min~~.~~}} = 6 \times 24 = 144<~~/~~math>~~

	~~===Equation~~ for ~~the angle between the hands===~~
	~~The angle between the hands can be found using the formula:~~

	~~<math>\begin{align}~~
	~~\Delta\theta~~
	~~&= \left\|\theta_{\text{hr}}~~ - ~~\theta_{\text{min.}}\right\| \\~~
	~~&= \left\|\frac{1}{2}(60H + M)~~ - ~~6M\right\|\\~~
	~~&= \left\|\frac{1}{2}(60H - 11M)\right\|~~
	~~\end{align}</math>~~

	~~where~~
	* <math>\scriptstyle H</math> is the hour
	* <math>\scriptstyle M</math> is the ~~minute~~

	~~====Example====~~
	~~The time is 2:20.~~

	~~<math>\begin{align}~~
	~~\Delta\theta~~
	~~&= \left\|\frac{1}{2}(60 \times 2~~ - ~~11 \times 20)\right\|\\~~
	~~&= \left\|\frac{1}{2}(120~~ - ~~220)\right\|\\~~
	~~&= 50~~
	~~\end{align}</math>~~

	~~===When are the hour and minute hands of a clock superimposed?===~~
	~~The hour and minute hands are superimposed only when their angle is the same.~~

	~~<math>\begin{align}~~
	~~\theta_{\text{hr}} &= \theta_{\text{min.}}\\~~
	~~\Rightarrow \frac{1}{2}(60H + M) &= 6M\\~~
	~~\Rightarrow 11M &= 60H\\~~
	~~\Rightarrow M &= \frac{60}{11}H\\~~
	~~\Rightarrow M &= 5.\overline{45}H~~
	~~\end{align}</math>~~

	<math>\scriptstyle H</math> is an integer in the range 0–11. This gives times of: 0:00, 1:05.{{overline\|45}}, 2:10.{{overline\|90}}, 3:16.{{overline\|36}}, etc. (0.{{overline\|45}} minutes are exactly 27.{{overline\|27}} seconds.)

	~~==See also==~~
	*[[Clock position]]

	~~==External links==~~
	* http://www.delphiforfun.org/Programs/clock_angle.htm
	* http://www.ldlewis.com/hospital_clock/ - ~~extensive clock angle analysis~~
	* http://www.jimloy.com/puzz/clock1.~~htm~~

	~~[[Category:Mathematics education]]~~
	~~[[Category:Elementary mathematics]]~~
	~~[[Category:Elementary geometry]]~~
	~~[[Category:Mathematical problems]]~~
	~~[[Category:Clocks]~~]

en>CRGreathouse: template inline

2013-10-20T16:40:10Z

template inline

← Older revision		Revision as of 18:40, 20 October 2013
Line 1:		Line 1:
	The ~~person who wrote~~ the ~~post~~ is ~~known as Jayson Hirano and he completely digs that name~~. ~~Ohio~~ is ~~exactly~~ where ~~her house~~ is. ~~I am an invoicing officer and I~~'ll be ~~promoted soon~~. ~~One~~ of the ~~extremely very best psychic readings~~ ([http://~~checkmates~~.co.za/~~index~~.~~php?do=~~/~~profile-56347~~/~~info~~/ http://~~checkmates~~.co.za/]~~) issues in the world for him is doing ballet and he'll be beginning some thing else alongside with it.~~		{{unreferenced\|date=October 2013}}

			[[Image:clockAngles.jpg\|thumb\|The diagram shows the angles formed by the hands of an analog clock showing a time of 2:20]]
			'''Clock angle problems''' are a type of [[mathematical problem]] which involve finding the angles between the hands of an [[analog clock]].

			==Math problem==
			Clock angle problems relate two different measurements: [[angle]]s and [[time]]. The angle is typically measured in [[degree (angle)\|degrees]] from the mark of number 12 clockwise. The time is usually based on [[12-hour clock]].

			A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute.

			===Equation for the angle of the hour hand===
			<math>\theta_{\text{hr}} = \frac{1}{2}M_\Sigma = \frac{1}{2}(60H + M)</math>

			where:
			* <math>\scriptstyle\theta</math> is the angle in degrees of the hand measured clockwise from the 12 o'clock position.
			* <math>\scriptstyle H</math> is the hours past 12 o'clock.
			* <math>\scriptstyle M</math> is the minutes past the hour.
			* <math>\scriptstyle M_\Sigma</math> is the minutes past 12 o'clock.

			===Equation for the angle of the minute hand===
			<math>\theta_{\text{min.}} = 6M</math>

			where:
			* <math>\scriptstyle\theta</math> is the angle in degrees of the hand measured clockwise from the 12 o'clock position.
			* <math>\scriptstyle M</math> is the minute.

			====Example====
			The time is 5:24. The angle in degrees of the hour hand is:

			<math>\theta_{\text{hr}} = \frac{1}{2}(60 \times 5 + 24) = 162</math>

			The angle in degrees of the minute hand is:

			<math>\theta_{\text{min.}} = 6 \times 24 = 144</math>

			===Equation for the angle between the hands===
			The angle between the hands can be found using the formula:

			<math>\begin{align}
			\Delta\theta
			&= \left\|\theta_{\text{hr}} - \theta_{\text{min.}}\right\| \\
			&= \left\|\frac{1}{2}(60H + M) - 6M\right\|\\
			&= \left\|\frac{1}{2}(60H - 11M)\right\|
			\end{align}</math>

			where
			* <math>\scriptstyle H</math> is the hour
			* <math>\scriptstyle M</math> is the minute

			====Example====
			The time is 2:20.

			<math>\begin{align}
			\Delta\theta
			&= \left\|\frac{1}{2}(60 \times 2 - 11 \times 20)\right\|\\
			&= \left\|\frac{1}{2}(120 - 220)\right\|\\
			&= 50
			\end{align}</math>

			===When are the hour and minute hands of a clock superimposed?===
			The hour and minute hands are superimposed only when their angle is the same.

			<math>\begin{align}
			\theta_{\text{hr}} &= \theta_{\text{min.}}\\
			\Rightarrow \frac{1}{2}(60H + M) &= 6M\\
			\Rightarrow 11M &= 60H\\
			\Rightarrow M &= \frac{60}{11}H\\
			\Rightarrow M &= 5.\overline{45}H
			\end{align}</math>

			<math>\scriptstyle H</math> is an integer in the range 0–11. This gives times of: 0:00, 1:05.{{overline\|45}}, 2:10.{{overline\|90}}, 3:16.{{overline\|36}}, etc. (0.{{overline\|45}} minutes are exactly 27.{{overline\|27}} seconds.)

			==See also==
			*[[Clock position]]

			==External links==
			* http://www.delphiforfun.org/Programs/clock_angle.htm
			* http://www.ldlewis.com/hospital_clock/ - extensive clock angle analysis
			* http://www.jimloy.com/puzz/clock1.htm

			[[Category:Mathematics education]]
			[[Category:Elementary mathematics]]
			[[Category:Elementary geometry]]
			[[Category:Mathematical problems]]
			[[Category:Clocks]]

en>ZéroBot: r2.7.1) (robot Adding: ca:Constant dels inversos de Fibonacci

2011-09-06T05:58:35Z

r2.7.1) (robot Adding: ca:Constant dels inversos de Fibonacci

New page

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