EQUIANGULAR SPIRAL
Definition Of Equiangular Spiral
An Equiangular Equiangular Spiral is a curve that forms a constant angle between a line from origin to any point on the curve and the tangent at that point. Equiangular Equiangular Spiral is also found in nature like nautilus.
More About Equiangular Spiral
In polar coordinate, the equation of an equiangular Equiangular Spiral is given as r = aebθ, where r is the distance from the origin, θ is the angle with the x-axis, and a and b are arbitrary constants.
The Equiangular Equiangular Spiral is also known as Bernoulli Equiangular Spiral, logarithmic Equiangular Spiral or logistique (in French).
Video Examples:Logarithmic Equiangular Spiral
Example of Equiangular Spiral
The figure shown below is of Chambered nautilus which is found in equiangular Equiangular Spiral shape in nature.
Solved Example on Equiangular Spiral
Ques: Identify the equiangular Equiangular Spiral in the figure shown.
Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D.Figure 4
Correct Answer: D
Solution:
Step 1: An Equiangular Equiangular Spiral is a curve that forms a constant angle between a line from origin to any point on the curve and tangent at that point.
Step 2: Among the figures, Figure 4 shows the equiangular Equiangular Spiral.
Quick Summary
- Also known as a logarithmic spiral or Bernoulli spiral.
- Found in nature, such as in nautilus shells.
🍎 Teacher Insights
Use real-world examples, such as nautilus shells, to illustrate the concept. Emphasize the constant angle property.🎓 Prerequisites
- Polar Coordinates
- Exponential Functions
- Trigonometry
Check Your Knowledge
Q1: Which of the following is an example of an equiangular spiral?
Frequently Asked Questions
Q: What is the equation of an equiangular spiral in polar coordinates?
A: The equation is r = ae^(bθ), where r is the distance from the origin, θ is the angle with the x-axis, and a and b are constants.