The notion of beauty has historically led many mathematicians to fruitful work. Yet, I have yet to find a mathematical text which has attempted to elucidate what exactly makes certain geometric figures aesthetically pleasing and others less so. Naturally, some would mention the properties of eleg...

Is there a dense subset $A$ of arbitrary given closed Jordan curve of $C$ on a plane which for each point member of $A$ like $p$ we have the following property: If we rotate $C$ around $p$ by $90^{\circ}$ clockwise on the plane then the created curve $C'$ has no intersection with $C$ exept on $p...