-
Logarithmic Spiral and Fibonacci Numbers
- An Equiangular Spiral
- An equiangular spiral - parametric equation
- Pedal and Co-pedal curve of the logarithmic spiral
- Measuring Equiangular Spirals in Nature
- The Equiangular Spiral in Plants - Fibonacci Numbers
- Flight of a Bee - Parallel Rays
- Flight of an Insect - Radial Source of Light
- Fibonacci Numbers and the Fibonacci Spiral
- Fibonacci Numbers and the Golden Spiral - demonstration
- The Flight of Insects. Conchospirals
- Sunflowers and Special Numbers
- Gnomonic Growth of the Nautilus
This activity is also part of one or more other Books. Modifications will be visible in all these Books. Do you want to modify the original activity or create your own copy for this Book instead?
This activity was created by '{$1}'. Do you want to modify the original activity or create your own copy instead?
This activity was created by '{$1}' and you lack the permission to edit it. Do you want to create your own copy instead and add it to the book?
Logarithmic Spiral and Fibonacci Numbers
Irina Boyadzhiev, Oct 1, 2014
Logarithmic Spiral and Fibonacci Numbers
-
1. An Equiangular Spiral
-
2. An equiangular spiral - parametric equation
-
3. Pedal and Co-pedal curve of the logarithmic spiral
-
4. Measuring Equiangular Spirals in Nature
-
5. The Equiangular Spiral in Plants - Fibonacci Numbers
-
6. Flight of a Bee - Parallel Rays
-
7. Flight of an Insect - Radial Source of Light
-
8. Fibonacci Numbers and the Fibonacci Spiral
-
9. Fibonacci Numbers and the Golden Spiral - demonstration
-
10. The Flight of Insects. Conchospirals
-
11. Sunflowers and Special Numbers
-
12. Gnomonic Growth of the Nautilus
An Equiangular Spiral
An equiangular spiral, also known as a logarithmic spiral is a curve with the property that the angle between the tangent and the radius at any point of the spiral is constant.
In polar coordinates: where and are positive real constants.
In parametric form: where and are real numbers.
- Move the point over the spiral to see the constant angle between the radius and the tangent.
- Consider a>0; a<0;
- α>90°, α<90°, α=90°.
An Equiangular Spiral
Saving…
All changes saved
Error
A timeout occurred. Trying to re-save …
Sorry, but the server is not responding. Please wait a few minutes and then try to save again.