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How have fractals effected science?

Fractals that which includes the fourth dimension and with which we can identify that our body's veins and nature are self similar.


Fractals are objects that are composed of what kind of elements?

self-similar


How do the ratios of side lenghts compare for triangles that are not similar?

There are no ratios that can be used for triangles that are not similar.


What are the types of fractals?

Fractals can be categorized into several types, including self-similar fractals, which exhibit the same pattern at different scales, and space-filling fractals, which cover a space completely. Other types include deterministic fractals, generated by a specific mathematical formula, and random fractals, which are created through stochastic processes. Notable examples include the Mandelbrot set and the Sierpiński triangle. Each type showcases unique properties and applications in mathematics, nature, and art.


How do ratios of side lengths compare for similar triangles?

they both have the same ratios


How can you use ratios of adjacent sides to prove if two rectangles are similar?

You can use ratios of adjacent sides to prove if two rectangles are similar by comparing to see if the ratios are the same


Why do similar triangles have the same trigonometric ratios?

Trigonometric ratios are characteristics of angles, not of lengths. And, by definition, the corresponding angles an similar triangles have the same measures.


What are fractals of pi?

Pi is a number. There are no fractals of pi.


How are mountains and crystals fractals?

Crystals are usually not fractals.


The ratios of parts of similar pyramids are equal?

corresponding


The of corresponding parts of similar pyramids are equal?

ratios


Are fractals real and how do they manifest in nature?

Fractals are real mathematical patterns that repeat at different scales. They manifest in nature through shapes like ferns, clouds, and coastlines, where similar patterns are seen at both small and large scales.