Maths and Art, a virtuous relationship - Symmetry and Patterns
Hi friends!
Obviously, the representation of geometric shapes is not art in itself but it is the basis for it, as we will see further... Starting from a division into six circle parts, we can draw a regular polygon of six sides. Observe how starting from a division into six parts of a circle we can draw a regular polygon of six sides (hexagon).
The knowledge provided by the postulates of geometry and mathematical theorems together with the invention of new measuring and drawing instruments as well as new calculation formulas have stimulated artistic creativity, which has given rise to new aesthetic approaches which, in turn, at the same time, they have awakened the need to find mathematical formulations of them, as is the case of Symmetry and Patterns for example, this being a good example of the virtuous relationship between mathematics and art.
No doubt many of the geometric shapes were first represented intuitively and surfaces were covered with patterns and symmetries empirically. Geometric formulas have later been represented graphically, such as the famous Pythagorean theorem for the right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.This is the graphic expression of that famous Pythagorean theorem.
It's also possible to draw a star of six points, or, if you want we can define this as two opposite equilateral triangles (symmetry).
Then, tracing three radial segments we obtain three identical rhomboids (pattern and symmetry).
Even further, by juxtaposing the hexagon and the six-point star, we get a shape made from several smaller shapes that make different radial symmetry patterns.
The same for the shape composed from the juxtaposition of three different shapes.
Some tips here:
Watch this demo.
Which is the simplest shape possible? What is the minimum quantity of sides to draw a shape? How to draw a regular shape (all the sides equal)?
Questions like these find the answer in the geometry.
In math, a pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.
Patterns exist all around us. We can find a pattern in the trees, in the window frames, on the floor, in our clothes, etc. One such real-life example is the zebra pattern.
Patterns can be finite and infinite.
Mathematically, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first. There can also be symmetry in one object, such as a face.
Let’s look at some examples of patterns and symmetry:
Patterns and symmetry here (how to do):
I wish you a very nice day!
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I think some kids may discover the magic of mathematic in childhood and that is the best time to introduce math in playing way. Actually everything needs to be done in playing way so that it is not too boring. A lot depends of the teachers and of course, on us parents. Very good video with demonstration how to do the triangle. Thank you for that educational post.
Thanks to you Stef! I agree with your thought.