Formula of curvature

In summary, the formula of curvature is a mathematical expression represented by the Greek letter "kappa" (κ) that calculates the degree of curviness of a curve or surface at a specific point. It is used in various fields of science, including physics, mathematics, and engineering, to describe the curvature of objects and trajectories. Positive curvature occurs when the curve or surface is bent outward, while negative curvature occurs when it is bent inward. The formula can be applied to three-dimensional objects by calculating the curvature along a specific plane. Real-life applications of the formula include structural design, optics, and geology.
  • #1
chetzread
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1

Homework Statement



can someone explain how to turn the formula of curvature T'(t) / r'(t) into | r'(t) x r"(t) | / | (r't)^3 | ?

Homework Equations

The Attempt at a Solution


my working is in 317.jpgT'(t) / r'(t) <blockquote class="imgur-embed-pub" lang="en" data-id="a/q3t1U"><a href="//imgur.com/q3t1U"></a></blockquote><script async src="//s.imgur.com/min/embed.js" charset="utf-8"></script>

[PLAIN]http://imgur.com/a/q3t1U[/B] [Broken]
 

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@chetzread -- Please post this in your other thread. Thank you.
 

What is the formula of curvature?

The formula of curvature is a mathematical expression that calculates the degree of curviness of a curve or surface at a specific point. It is represented by the Greek letter "kappa" (κ) and is calculated by dividing the radius of curvature at a point by the length of the curve at that point.

How is the formula of curvature used in science?

The formula of curvature is used in various fields of science, such as physics, mathematics, and engineering. It is used to describe the curvature of objects, surfaces, and trajectories, and is essential in understanding and analyzing the behavior of natural and man-made structures.

What is the difference between positive and negative curvature?

Positive curvature occurs when the curve or surface is bent outward, like a sphere. Negative curvature occurs when the curve or surface is bent inward, like a saddle. The sign of the curvature is determined by the direction in which the curve or surface is bending at a specific point.

Can the formula of curvature be applied to three-dimensional objects?

Yes, the formula of curvature can be applied to three-dimensional objects. In this case, the curvature is calculated along a specific plane, known as the principal plane, which is perpendicular to the direction of bending.

Are there any real-life applications of the formula of curvature?

Yes, the formula of curvature has various real-life applications, such as in the design of bridges, roads, and buildings to ensure structural stability. It is also used in optics to calculate the curvature of lenses and in geology to describe the shape of landforms.

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