The Perigonal angles , Also known as complete and whole, are those in which the sides of their angle coincide, equal to four right angles that measure 360 °.
In plane geometry, an angle is a figure made up of two line segments, called semi-lines, which are joined at one end: the vertex.
To distinguish between these lines, they are indicated by the letters A and B, where A is the origin point (the half-rectangle that remains fixed) and B is the end point (the half-rectangle that moves to form the aperture).
The aperture between the line segments forming part of an angle is measured in degrees (°) and is called the amplitude; This measure allows to classify the angles into four types:
1 - Acute angles: they have an amplitude smaller than 90 °.
2 - Straight angles: they have an amplitude of 90 ° exactly.
3 - obtuse angles: they have an amplitude greater than 90 ° and less than 180 °.
4 - Concave angles:
- Flat angles: have an amplitude of 180 °.
Reflex angles: have an amplitude greater than 180 ° but less than 360 °.
- Perigonal angles: they have an amplitude of 360 °. They are also called whole angles and whole angles.
In this sense, it is observed that the perigonal angle, when measuring 360 °, forms a circumference. Likewise, the perigonal angles may result from the sum of other angles of lesser amplitude, for example, four right angles form a perigonal one.
The perigonal angle is a concave angle
The concave angles are those having an amplitude between 180 ° and 360 °.
In this sense, there are three types of concave angles: the plains (180 °), the reflections (greater than 180 ° but less than 360 °) and the perigonal ones (360 °).
The perigonal angle and the circumferences
The perigonal angle is equal to the amplitude of a circumference, that is to say 2 radians (360 °). This means that the perigonal angles are formed when one of the semi-courses makes a complete rotation with respect to the other half-right, positioning itself on it. For example, the hands of the clocks form perigonal angles.
In this sense, just like the circumferences, the perigonal angles can be subdivided into quadrants (1/4 of the circumference), radians (1/2 of the circumference), among other divisions.
Starting at point 0.1 and continuing counterclockwise. It presents a perigonal angle and its possible subdivisions.
The perigonal angle: end and origin
As explained above, in every angle there is a semi-rectum called the end and another called the origin. AND
N the perigonal angles, the end and the origin are in the same position, since the end has made a complete rotation with respect to the origin.
The perigonal angle and the consecutive angles
The consecutive angles are those that share one side in common, that is, the half-rectum of one is the same half-right of the other.
The perigonal angles can be formed by a series of consecutive angles that, together, complete the 360 °.
For example:
- Two angles of 180 ° = a perigonal angle
- Three angles of 120 ° = a perigonal angle
- Four angles of 90 ° = a perigonal angle
- Five angles of 72 ° = a perigonal angle
- Six angles of 60 ° = a perigonal angle
And so on.
It should be noted that the angles that make up the perigonal do not necessarily have to have the same amplitude.
For example, a series of four consecutive angles having an amplitude of 30 °, 80 °, 100 ° and 150 ° (360 ° in total) is also a perigonal angle.
Example of addition of several consecutive angles of different amplitudes to form a perigonal angle.
Examples of perigonal angles
In our day to day, we are surrounded by objects that measure 360 ° and, therefore, can be perigonal angles. Here are some examples of these:
1- The wheels
The wheels of bicycles, automobiles and other vehicles are examples of perigonal angles. In addition, the wheels of the bicycles and the automobiles have dividing lines that could be understood as series of consecutive angles.
2- A hand clock
Analog clocks have rotating hands to set the time. Take into account a second hand and a minute hand when they are positioned on the number 12 of the clock, indicating the first second of a minute.
Seconds move at a rate of 6 ° per second, which means that after the minute the needle will have traveled 360 °.
In this example, the minute hand and the second hand are the two half-angles of an angle: the minute hand has been held in position, while the second hand has made a complete turn, creating a perigonal angle.
For its part, a minute takes 60 minutes to complete a perigonal angle with respect to the hand that marks the hour.
3- Steering wheels and rudders
The steering wheels of the automobiles and the rudders of the ships are also samples of perigonal angles.
As with a bicycle wheel, some steering wheels and rudders have segments that could act as consecutive angles.
Rudder of a boat with eight consecutive 45 ° angles.
4- The blades of a fan or windmill
Typically, these systems have three or four blades. In case of presenting three blades, these are three consecutive angles of 120 °; If it has four, they will be consecutive 90 ° angles.
5- The reels of a video camera
The reels of a video camera have three radial divisions of 120 ° each. The sums of the angles created by these divisions give rise to a perigonal angle.
References
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- Perigon. Retrieved on June 2, 2017, from memidex.com.
- Perigon. Retrieved on June 2, 2017, from thefreedictionary.com.
- Angle. Retrieved on June 2, 2017, from en.wikipedia.org.
- Full angle. Retrieved on June 2, 2017, from mathworld.wolfram.com.
- Angles. Retrieved on June 2, 2017, from mathteacher.com.au.
- Perigon. Retrieved on June 2, 2017, from merriam-webster.com.
- Perigon. Retrieved on June 2, 2017, from dictionary.com.