During the last years of the 1910s, Hilma af Klint created several series of small paintings in which she systematically explored an abstract idiom with the help of ruler and compasses. The triangles, squares, circles, and ellipses that appear here in constantly new constellations express a spiritual dynamic, according to af Klint’s notebooks from these years. Hilma af Klint considered this work a kind of research, and she used ‘spiritual scientific’ methods – a term borrowed from anthroposophy – in order to understand the evolution and development of mankind. In her studies of living beings, she gained insight into an abstract world of geometrical conditions and guidelines.
The reason theres no precise equation for the perimeter of an ellipse is because the practical, real-world manner in which to produce an ellipse is to cut a cylinder at an angle. This would require third-dimensional rotational geometry, or mathematics that cannot be produced only on a two-dimensional plane. Meaning the originally problem is missing key information. (which can be expressed by numbers on a two dimensional plane, but only after the unique ellipse is produced and measured.)
Sometimes you will be provided a mathematically and fundamentally incomplete data set. You will either have to say that the problem is impossible or guess; depending on the circumstances and moralistic understanding of the problem.
P.S.
Imagine being a 2D creature finding an elliptical object. You can only interact with 2D object, and this thing is immeasurable. Alternatively, how deep is your personal gravitational well?
“That sounds like a good idea…….”-“Is there something bothering you with the idea?”-“No, the idea is GOOD…..”
Can someone explain this to me?
Old people use quotation marks to indicate emphasis, as a substitute for italics (which many of them could not produce on the old typewriters they learned to write on), whereas young people use them to indicate sarcasm or falseness. They’re used as “scare quotes”.
And old people use ellipses simply to indicate a pause, or for some other incomprehensible reason I’m not aware of. But young people use ellipses to indicate passive-aggression.
So an old person could type something like:
how are things going with your “boyfriend”….
and what they mean is
How are things going with your boyfriend? [Im so excited for you, sweetie, and I wanna hear about it]
But a young person would interpret that sentence as
How are things going with your so-called boyfriend…. [I say, while seething with contempt for him and possibly for you too]
The linguistic difference across generations is beautifully explained here thank you
