diiferential geometry

shahar

shahar

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In the link: https://www.intmath.com/functions-and-graphs/introduction-to-geometry.php
under the title "5. Differential Geometry"
Perhaps the easiest way to think about this is to imagine a screw. A screw has a solid shaft in the middle surrounded by the helical thread. The thread allows the screw to pull itself into another material. Because the thread is not on a singular plane, you can't get an accurate measurement for the radius without understanding how the curvature of curves and surfaces work.

Can someone explain the underlined sentence?
 
The helical thread of the screw has this shape (open the link):

mathworld.wolfram.com

Helix -- from Wolfram MathWorld

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides...
mathworld.wolfram.com

You will need to understand the formulas below to understand the behavior of the radius of that shape. In simple words, to understand a geometrical shape, you will need to understand its curvature and torsion.
 
mario99 said:
The helical thread of the screw has this shape (open the link):

mathworld.wolfram.com

Helix -- from Wolfram MathWorld

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides...
mathworld.wolfram.com

You will need to understand the formulas below to understand the behavior of the radius of that shape. In simple words, to understand a geometrical shape, you will need to understand its curvature and torsion.
Click to expand...
What is the definition of thread?
It is not clear to me.
 
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