#conic — Public Fediverse posts

The ‘Conics’ of Apollonius of Perga (c.260–c.190 BCE) became the standard text for ‘conic sections’ — the curves formed by the intersection of a plane and a cone, namely an ellipse, parabola, or hyperbola, depending on the angle of the plane relative to the slope of the cone (see attached image).

In the preface to the ‘Conics’, Apollonius wrote:

‘The third book contains many incredible theorems of use for the construction of solid loci and for limits of possibility of which the greatest part and the most beautiful [kallista κάλλιστα] are new.’

This quotation is triply important in the historiography of mathematical beauty: (1) it is the earliest extant description of a mathematical theorem as ‘beautiful’; (2) it is the earliest extant application of the term ‘beautiful’ to mathematics by a mathematician; and (3) it is the unique extant use of the term ‘beautiful’ to describe theorems by an ancient Greek mathematician.

(There is much discussion of the beauty of mathematics in ancient Greek thought, but it normally applies to the objects or concepts of mathematics.)

[Each day of February, I intend to post an interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

1/3

#MathematicalBeauty #HistMath #Conic #ConicSection #geometry #aesthetics

"If the Greeks had not cultivated conic sections, Kepler could not have superseded Ptolemy." – William Whewell (1794–1866)
#quote #mathematics #conic #maths #math

"If the Greeks had not cultivated conic sections, Kepler could not have superseded Ptolemy." – William Whewell (1794–1866)
#quote #mathematics #conic #maths #math

Day 4 - section:

when we see sections

of ourselves — our potential

manifests loci

https://codepen.io/fractalkitty/pen/wvRxORX

#mathober2023 #section #conic #hyperbola #p5js #procreate #codepen #math #mathart #loci #haiku #poetry

@bodhidave @EgyptianAphorist @mcmullin @clarablackink @histodons
Mathematics and #art are human activities, and in a #mathematics paper
(on #conic sections, the #conics, in particular, and described in the
linked blog post), I was pleased to have reason to quote what
Robert Pirsig said about teaching #writing. I commented,

> What #Pirsig wanted, as an English teacher, was for students to learn
> to write what *they* wanted. In the end, this would be what everybody
> else wanted, which was *quality.*

But there's a difference:

> In mathematics, an essential part of #quality is *truth,* or
> *correctness* if you prefer. We take this to be universal.

Not everybody may agree on what is good art, but I think they should
agree on what is correct mathematics.

https://polytropy.com/2020/08/05/an-exercise-in-analytic-geometry/