Maths and Art, a virtuous relationship - Geometry, II
Hi friends!
We aim to draw a square in the centre of a surface. No matter the surface size, it can be a big surface like a terrain to build, a wall, or a small one, like a canvas surface or a drawing paper.
Imagine we are in the time of the beginnings of geometry concepts and imagine that we don't have any measurement tools, and also imagine that we only dispose of a rope as a measurement tool, nothing, absolutely nothing more.
Let's start...
Diagonally crossing the "rope" from the top left corner to the bottom right corner, then crossing the rope from the top right corner to the bottom left corner, we find the centre of the surface we have chosen to draw, here the centre is marked with a cross red.
Now we can draw a horizontal line, which will be located in the middle of the height of the drawing surface.
By drawing two points equally spaced in the centre of the horizontal line as shown below we can measure the distance with our "rope" represented here by the red line.
Now we use this measurement to draw a cross above the horizontal line and another at the bottom.
Those two points marked allow us to draw a vertical line to divide the surface into four equal parts.
Using a similar process we divide the surface again to obtain eight equal parts.
By measuring from the centre to a certain point as shown below, we obtain a new reference that allows us to draw a circle that will mark the same distance on all the lines we have drawn on the surface.
Finally, we use the four points of intersection between the circle and the diagonals to draw the lines necessary to make a rectangle with four equal sides (that is, we have drawn a square)
Here is our finished square.
Well, the objective was to think or imagine how artists, architects, sculptors, builders, etc., solved the technical problems that arose in their creative process, using the knowledge of geometry and mathematics provided by brilliant minds like Euclid, who knew how to organize, logically and systematically, the knowledge of even older cultures such as that of Egypt, among others.
Little by little this relationship between art and mathematics will become more evident, you will see...
You will notice already that this knowledge is in use until our days by artists.
For a more detailed explanation of this process, here is a link to a previous lesson on this topic:
Or if you want to delve deeper into this interesting and useful topic for artists, I suggest you look up Euclidean Geometry.
I wish you a very nice day!
Peace Is Over
by J.Van de Perre - video demo, painting process
Herbarium
I recall the time of geometry with my son when he was in school and we also did the same task, it was very exciting to see how kids get excited when they see that using a pencil that was tied up on the other that was placed in centre and this way it was showed how using simple tools it could replace a modern compass.
Thank you, friend!
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Thank you for the lesson! I'll run and draw some squares :)
Great!