# Results for: “Mathematics”

Title | Author | Publisher | Format | Buy | Remix | ||
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## Medians, Altitudes, Bisectors: Praxis I Geometry |
Ace Academics | Ace Academics | ePub | ||||

## 4 |
Parmananda Gupta | Laxmi Publications | |||||

2 Curvature and Torsion 1. INTRODUCTION For curves in space, the concepts of curvature and torsion are of fundamental importance. We know that line segments are uniquely determined by their lengths, circles by their radii, triangles by side-angle-side etc. In geometry, we look for geometric quantities which distinguish one figure from another. The importance of curvature and torsion can easily be estimated from the fact that it can be proved that a curve is uniquely determined (except for its position in space) if its curvature and torsion are given as continuous functions of arc length ‘s’. 2. CURVATURE OF A CURVE Let r = r(s) be a regular curve C of class Cm(m ≥ 2), where s is the parameter ‘arc length’. The vector r″(s) is called the curvature vector on the curve C at the point r(s) and it is denoted by t(s) κ(s) (or by κ). The magnitude of the curvature vector r(s) is called the curvature of the curve C at the point r(s) and it is denoted by κ(s) (or by κ). C k(s) ∴ κ(s) = |r″(s)| Also t(s) = r′(s), so we have See All Chapters |
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## Real Numbers: SAT Arithmetic |
Ace Academics | Ace Academics | ePub | ||||

## Ratio and Proportion: COOP-HSPT Algebra |
Ace Academics | Ace Academics | ePub | ||||

## Signed Numbers: CLEP Algebra I |
Ace Academics | Ace Academics | ePub | ||||

## Multiplication: Whole Numbers: SAT Arithmetic |
Ace Academics | Ace Academics | ePub | ||||

## Triangles: GRE Geometry |
Ace Academics | Ace Academics | ePub | ||||

## Advanced Equations: CLEP Algebra I |
Ace Academics | Ace Academics | ePub | ||||

## Factoring Polynomials: CLEP Algebra I |
Ace Academics | Ace Academics | ePub | ||||

## Subtraction: Fractions: GED Arithmetic |
Ace Academics | Ace Academics | ePub | ||||

## Evaluating Formulas: GRE Algebra |
Ace Academics | Ace Academics | ePub | ||||

## Equations with Several Variables: GED Algebra |
Ace Academics | Ace Academics | ePub | ||||

## Properties of Numbers: GRE Algebra |
Ace Academics | Ace Academics | ePub | ||||

## Simultaneous Equations: GED Algebra |
Ace Academics | Ace Academics | ePub | ||||

## Properties of Numbers: Praxis I Algebra |
Ace Academics | Ace Academics | ePub | ||||