Why Does Mathematics Favor Perfect Shapes to Model Imperfect Nature?

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SUMMARY

Mathematics often utilizes perfect shapes such as spheres, triangles, and squares to model the imperfect nature of the world. While the Earth is not a perfect sphere, these geometric shapes serve as effective approximations for various applications in architecture and engineering. The discussion highlights the role of fractal geometry and natural patterns, including spirals and the Fibonacci series, in understanding complex shapes found in nature. Ultimately, mathematics provides a foundational framework for approximating reality through idealized forms.

PREREQUISITES
  • Understanding of basic geometric shapes such as circles, triangles, and squares.
  • Familiarity with fractal geometry and its applications.
  • Knowledge of the Fibonacci series and its relevance in natural patterns.
  • Basic principles of measurement and area calculation in geometry.
NEXT STEPS
  • Explore the principles of fractal geometry and its applications in modeling natural phenomena.
  • Research the Fibonacci series and its occurrence in biological systems.
  • Learn about the mathematical modeling of irregular shapes using calculus.
  • Investigate the relationship between geometry and architecture in design principles.
USEFUL FOR

Mathematicians, architects, engineers, and anyone interested in the intersection of mathematics and natural phenomena will benefit from this discussion.

Niaboc67
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Why does mathematics deal with the world of perfect spheres, triangles and squares. I understand how this can be applied to architecture and engineering. But this seems counter-intuitive to 'nature' that surrounds us which is objects that are not perfect in shape. The Earth for instance isn't a perfect sphere it budges out at the equator. So why is mathematics always prone to using perfect angles and objects to be measured when nature isn't that way at all.

Thank you
 
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Mathematics uses other shapes, too. But often, circles, triangles and so on are good approximations. In addition, they are used as introduction as they are easier to treat than other shapes.

The Earth for instance isn't a perfect sphere it budges out at the equator.
Plus many more corrections to the shape.
 
nature isn't that way at all.

That is what inspired fractal geometry.

Natural geometry also follows some more specialised mathematics - spirals, fibonacchi series, and some very complicated equal area shpes.

Note also that the word geometry derives from 'measurement of the Earth'.
 
Niaboc67 said:
Why does mathematics deal with the world of perfect spheres, triangles and squares. I understand how this can be applied to architecture and engineering. But this seems counter-intuitive to 'nature' that surrounds us which is objects that are not perfect in shape. The Earth for instance isn't a perfect sphere it budges out at the equator. So why is mathematics always prone to using perfect angles and objects to be measured when nature isn't that way at all.

Thank you

Why should nature guide maths?
 
arildno said:
Why should nature guide maths?

I guess the way i see it is. I was mainly just wondering why math uses examples from natural world it's perfect objects seems a bit unrealistic. Though I am no mathematician i would think mathematics becomes so approximate that any shape of nature can be imagined.
 
And what should you approximate reality FROM, if not from the "perfect" shapes?

You can call a rectangle a perfect, unrealistic figure for all you like, but it is from the rectangle and its associated area formula that you can basically derive the area of any other shape.
 

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