Using geometeric series to get different shapes

In summary, the conversation discusses a final project for a math class and the use of geometric series to create different shapes. A website was mentioned as a possible resource, but it had already been used by the teacher. The person asking the question is looking for other options, specifically involving calculus, and the other person suggests the anti-snowflake and provides a website with various fractals as examples.
  • #1
minase
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We have this final project for my math class and I was thinking of using geometeric series to get different shapes. I found this great website http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/series/serapp.html but our teacher has already used it as an example. Do you know any other easy shapes I could do. Not involving :tongue: complex numbers...Julia Mandelbrot formula. It doesn't have to be about geometeric series it could be any thing that involves calculus.
 
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  • #2
You could do the anti-snowflake.
http://math.rice.edu/~lanius/frac/anti.html
 
  • #3
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1. How can geometric series be used to create different shapes?

Geometric series can be used to create different shapes by utilizing the concept of iteration. By starting with a simple geometric shape, such as a square, and repeatedly scaling and rotating it according to a specific sequence, more complex and unique shapes can be generated.

2. What is the formula for creating a geometric series?

The formula for a geometric series is a1 + a1r + a1r2 + ... + a1rn-1, where a1 is the initial term and r is the common ratio.

3. Can any shape be created using geometric series?

Technically, yes. However, the number of iterations and the specific sequence used will determine the complexity and accuracy of the final shape. Some shapes may require an infinite number of iterations to be fully realized.

4. What are some real-life applications of using geometric series to create shapes?

One real-life application is in computer graphics and animation. Geometric series can be used to generate complex and realistic 3D models, which are used in video games, movies, and other visual media. They are also used in the design of fractals and other mathematical art.

5. Are there any limitations to using geometric series to create shapes?

One limitation is the precision of the final shape, as it may not be an exact replica of the desired shape. Additionally, the sequence used to generate the shape may need to be adjusted for different starting shapes or to achieve a specific level of complexity.

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