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Nano-Passion
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We usually describe angles in two dimensions (x and y plane). What is the mathematics behind three dimensions?
I don't get it. You're an undergrad in physics and you're asking this question? Why don't you already know?Nano-Passion said:We usually describe angles in two dimensions (x and y plane). What is the mathematics behind three dimensions?
Jocko Homo said:I don't get it. You're an undergrad in physics and you're asking this question? Why don't you already know?
It's really no different. When you talk about the angle between things in three dimensions, you can think of them as being on some plane oriented in those three dimensions and then think about the angle in relation to that plane, just as you would with the familiar x-y plane...
Char. Limit said:Actually, I'd say we usually describe angles in two-dimensions with theta and r. That is, an angle from the designated "zero line", and a distance from the origin. In three dimensions, we simply add another angle, usually phi, that I call the "vertical angle", or the angle between the line and the x-y plane.
As you see, there is a very distinct loss of accuracy in 'acos' for angles
near pi. Some seven entire decimal places have been lost - that is,
errors are several million times as large as normal. On the other hand,
the angle near pi/2 yields the customary 1 in 2^52 accuracy.
Angles in three dimensions are angles that exist in three-dimensional space, meaning they involve three mutually perpendicular axes (x, y, and z). These angles are used to describe the orientation and rotation of objects in three-dimensional space.
Angles in three dimensions are typically measured using degrees or radians. Degrees are the most common unit of measurement and are based on dividing a circle into 360 equal parts. Radians are a mathematical unit of measurement based on the radius of a circle and are commonly used in advanced mathematics and physics.
A positive angle in three dimensions is measured counterclockwise from the reference axis, while a negative angle is measured clockwise. This convention is used to maintain consistency in mathematical calculations and ensure accurate results.
Angles in three dimensions play a crucial role in determining the shape and orientation of objects in space. They can be used to describe the rotation of objects around a specific axis, the tilt of surfaces, and the direction of forces acting on objects.
Angles in three dimensions have numerous real-world applications, including architecture, engineering, and computer graphics. They are also used in navigation and GPS technology, robotics, and video game development. Additionally, angles in three dimensions are essential in physics for understanding motion, energy, and forces.