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[[Image:Annulus_area.svg|right|150px|An annulus]]
We may have attempted and failed whenever we have attempted to drop certain fat. If you manage to shed a number of pounds we then have the complicated task of keeping the fat off. We are many likely following the wrong rules that is why our fat starts to grow again. Losing fat isn't too difficult plus really it is actually easy to do away with it plus keep it off should you recognize well what you're undertaking. Below I will inform you ways to drop weight effectively plus the means to keep it off.<br><br>There are many sites which create it simple to locate out how several calories we require for fat maintenance and fat reduction. Just type [http://safedietplans.com/bmr-calculator bmr calculator] into a search engine and follow the steps they provide you. BMR stands for basal metabolic rate, plus finding this amount can aid provide you an idea of how several calories you'll need to consume for the certain goals. You'll be asked to answer some issues about a activity level plus possibly even the degree of fat loss we want to achieve. Some BMR calculators may go thus far as to offer the amounts of proteins, carbohydrates plus fats you need to consume also. They're a very useful tool!<br><br>You could be man or woman, but you nevertheless require muscle mass to raise your basal metabolic rate. This is a measure of how various calories the body burns each day. Already you know which too countless unused calories are bad for the wellness, so you want to start to pay attention to how much muscle is on your body. It is worthwhile.<br><br>A low calorie diet could do you more damage than advantageous. If you are craving more calories, this will subsequently affect your metabolism. Where may the body get the stamina it requires? It might actually get energy from a muscle, because there are no food reserves available. When this occurs, it may be very detrimental to a health, because the proper way to lose fat is to gain muscle, not take it away.<br><br>Now let's calculate the number of calories your need to support the daily activities. Simply increase your calculated bmr by 1.2 should you don't exercise at all, 1.375 in the event you exercise lightly 1 to 3 times per week, 1.55 in the event you exercise moderately 3 to 5 occasions per week, 1.725 in the event you exercise hard 6 to 7 occasions per week, or 1.9 should you have a physically demanding job and exercise daily or are training for a sports competition including a marathon.<br><br>When you cut back on calories too much, the body could go into "starvation mode' inside that it starts storing everything we consume instead of burning from it for fuel. If you cut your calories too drastically you can see no fat reduction plus be tired or sluggish. To rev up your metabolism and let a body run effectively you must eat throughout the day plus make certain we are eating enough.<br><br>McArdle, William, Katch, Frank, and Katch, Victor. (1998). Exercise Physiology: Energy, Nutrition, plus Human Performance. Baltimore, Maryland: Williams plus Wilkins.
In [[mathematics]], an '''annulus''' (the [[Latin]] word for "little ring", with plural ''annuli'') is a ring-shaped object, especially a region bounded by two concentric circles. The adjectival form is '''annular''' (as in [[annular eclipse]]).
 
The open annulus is [[Homeomorphism|topologically equivalent]] to both the open [[cylinder (geometry)|cylinder]] {{math|''S''<sup>1</sup> &times; (0,1)}} and the [[punctured plane]].
 
The area of an annulus is the difference in the areas of the larger [[circle]] of radius {{math|''R''}} and the smaller one of radius {{math|''r''}}:
:<math>A = \pi R^2 - \pi r^2 = \pi(R^2 - r^2)\,.</math>
 
The area of an annulus can be obtained from the length of the longest interval that can lie completely inside the annulus, 2*''d'' in the accompanying diagram. This can be proven by the [[Pythagorean theorem]]; the length of the longest interval that can lie completely inside the annulus will be [[tangent]] to the smaller circle and form a right angle with its radius at that point. Therefore ''d'' and ''r'' are the sides of a right angled triangle with hypotenuse ''R'' and the area is given by:
:<math>A = \pi (R^2-r^2) = \pi d^2 \,.</math>
 
The area can also be obtained via [[calculus]] by dividing the annulus up into an infinite number of annuli of [[infinitesimal]] width {{math|''d&rho;''}} and area {{math|2''&pi;&rho; d&rho;''}} ( {{math|= circumference &times; width}}) and then [[integral|integrating]] from ''&rho;'' = ''r'' to ''&rho;'' = ''R'':
:<math>A = \int_r^R 2\pi\rho\, d\rho = \pi(R^2-r^2).</math>
 
The area of an annulus sector of angle {{math|''&theta;''}}, with {{math|''&theta;''}} measured in radians, is given by:
:<math> A = \frac{\theta}{2} (R^2 - r^2) </math>
 
==Complex structure==
In [[complex analysis]] an '''annulus''' {{math|ann''(a; r, R)''}} in the [[complex plane]] is an [[open region]] defined by:
 
:<math> r < |z-a| < R.\,</math>
 
If {{math|''r''}} is {{math|0}}, the region is known as the '''punctured disk''' of radius {{math|''R''}} around the point {{math|''a''}}.
 
As a subset of the complex [[Plane (mathematics)|plane]], an annulus can be considered as a [[Riemann surface]]. The complex structure of an annulus depends only on the ratio {{math|''r''/''R''}}. Each annulus {{math|ann''(a; r, R)''}} can be [[holomorphic function|holomorphically]] mapped to a standard one centered at the origin and with outer radius {{math|1}} by the map
:<math>z \mapsto \frac{z-a}{R}.</math>
The inner radius is then {{math|''r''/''R'' < 1}}.
 
The [[Hadamard three-circle theorem]] is a statement about the maximum value a holomorphic function may take inside an annulus.
 
== See also ==
* [[Annulus theorem]] (or conjecture)
* [[Spherical shell]]
* [[Torus]]
* [[List of geometric shapes]]
 
== External links ==
*[http://www.mathopenref.com/annulus.html Annulus definition and properties] With interactive animation
*[http://www.mathopenref.com/annulusarea.html Area of an annulus, formula] With interactive animation
 
[[Category:Elementary geometry]]
[[Category:Geometric shapes]]

Revision as of 21:30, 11 February 2014

We may have attempted and failed whenever we have attempted to drop certain fat. If you manage to shed a number of pounds we then have the complicated task of keeping the fat off. We are many likely following the wrong rules that is why our fat starts to grow again. Losing fat isn't too difficult plus really it is actually easy to do away with it plus keep it off should you recognize well what you're undertaking. Below I will inform you ways to drop weight effectively plus the means to keep it off.

There are many sites which create it simple to locate out how several calories we require for fat maintenance and fat reduction. Just type bmr calculator into a search engine and follow the steps they provide you. BMR stands for basal metabolic rate, plus finding this amount can aid provide you an idea of how several calories you'll need to consume for the certain goals. You'll be asked to answer some issues about a activity level plus possibly even the degree of fat loss we want to achieve. Some BMR calculators may go thus far as to offer the amounts of proteins, carbohydrates plus fats you need to consume also. They're a very useful tool!

You could be man or woman, but you nevertheless require muscle mass to raise your basal metabolic rate. This is a measure of how various calories the body burns each day. Already you know which too countless unused calories are bad for the wellness, so you want to start to pay attention to how much muscle is on your body. It is worthwhile.

A low calorie diet could do you more damage than advantageous. If you are craving more calories, this will subsequently affect your metabolism. Where may the body get the stamina it requires? It might actually get energy from a muscle, because there are no food reserves available. When this occurs, it may be very detrimental to a health, because the proper way to lose fat is to gain muscle, not take it away.

Now let's calculate the number of calories your need to support the daily activities. Simply increase your calculated bmr by 1.2 should you don't exercise at all, 1.375 in the event you exercise lightly 1 to 3 times per week, 1.55 in the event you exercise moderately 3 to 5 occasions per week, 1.725 in the event you exercise hard 6 to 7 occasions per week, or 1.9 should you have a physically demanding job and exercise daily or are training for a sports competition including a marathon.

When you cut back on calories too much, the body could go into "starvation mode' inside that it starts storing everything we consume instead of burning from it for fuel. If you cut your calories too drastically you can see no fat reduction plus be tired or sluggish. To rev up your metabolism and let a body run effectively you must eat throughout the day plus make certain we are eating enough.

McArdle, William, Katch, Frank, and Katch, Victor. (1998). Exercise Physiology: Energy, Nutrition, plus Human Performance. Baltimore, Maryland: Williams plus Wilkins.