> The name is also off-putting: juxtaposing super and hyper sounds silly. The etymology makes sense, even if it sounds funny. Piet Hein used the prefix super– to refer to increasing the exponent from the usual value of 2. Its unfortunate that hyperbola begins with a root that is similar to super.
> Its unfortunate that hyperbola begins with a root that is similar to super.
The choice of the word "similar" by the author is not really appropriate, because this is not a random similarity.
The words "super" and "hyper" mean exactly the same thing and they descend from a single Indo-European word, the former being the Latin variant and the latter being the Ancient Greek variant, while the corresponding English variant is "over".
"Superbola" would be ambiguous, because that could be a "superparabola".
I am among those who dislike the mixing of distinct languages inside a compound word when there is no need for that.
Therefore, while "superquadrics" is a correct term, instead of "superellipse" and "superhyperbola" I would prefer "hyperellipse" and "hyperhyperbola". And instead of "Superman", "Overman" :-)
How about just "superbola"? :-)