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Cody Richeson
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Because a triangle comes out to 180 degrees, and yet it can only have three sides. A circle has 360 degrees, but its number of "sides" are uncountable. Can someone explain this?
In the sense in which a triangle has 360 degrees a circle has an infinite number of degrees so you are comparing apples and oranges.Cody Richeson said:Because a triangle comes out to 180 degrees, and yet it can only have three sides. A circle has 360 degrees, but its number of "sides" are uncountable. Can someone explain this?
You are comparing apples and oranges. The "180 degrees" in a triangle is the sum of the three vertex angles. The "360 degrees" in a circle are measured at the center of the circle.Cody Richeson said:Because a triangle comes out to 180 degrees, and yet it can only have three sides. A circle has 360 degrees, but its number of "sides" are uncountable. Can someone explain this?
HallsofIvy said:You are comparing apples and oranges. The "180 degrees" in a triangle is the sum of the three vertex angles. The "360 degrees" in a circle are measured at the center of the circle.
No, not really. If you're measuring degrees, you're measuring an angle that a ray has rotated relative to some fixed direction. The degree measure has nothing to do with the length of the ray.Cody Richeson said:So any measurement of degrees radiating from a center point will necessarily be round?
Makes sense.
Cody Richeson said:So this is not the same for triangles, I suppose, or any polygon? What about a polygon with a very large number of sides that almost appears circular?
If by "round" you mean "adds up to 360" then the answer is yes. They're all 360 degrees.Cody Richeson said:So any measurement of degrees radiating from a center point will necessarily be round? Makes sense. So this is not the same for triangles, I suppose, or any polygon? What about a polygon with a very large number of sides that almost appears circular?
Circles are infinitely smooth because they have no corners or edges. In mathematics, a circle is defined as a set of points that are equidistant from a given point, called the center. This means that no matter how close you zoom in on a circle, it will always appear smooth and without any jagged edges.
Circles do not have degrees, but they can be measured in degrees. In geometry, a circle is divided into 360 equal parts, each representing 1 degree. This measurement is useful for calculating angles and arcs within a circle.
The degree measure is important for circles because it allows us to measure and understand the angles and arcs within a circle. This is crucial in many fields, such as engineering, architecture, and physics, where circles and their properties are used in calculations and designs.
No, circles are not the only shapes that are infinitely smooth. Any shape that is defined by a continuous, unbroken curve is considered infinitely smooth. This includes shapes such as ellipses, parabolas, and hyperbolas.
No, circles do not have different degrees. As mentioned earlier, a circle is divided into 360 equal parts, or degrees, and this measurement remains constant for all circles. However, the size or radius of a circle can vary, resulting in different circumferences and areas.