1. ## An terror curves

look at this curve:defined by this : $x^4+y^4=1$

how can we calculate the number of its vertexs , and length of its arc , the area that its surround.

and how can we paramelize it.

thanks very much

2. Originally Posted by Xingyuan
look at this curve:defined by this : $x^4+y^4=1$

how can we calculate the number of its vertexs , and length of its arc , the area that its surround.And how can we paramelize it.
thanks very much

You can parametrize it by $x = \sqrt{\sin t}$ and $y = \sqrt{\cos t}$

3. Originally Posted by Xingyuan
look at this curve:defined by this : $x^4+y^4=1$

how can we calculate the number of its vertexs , and length of its arc , the area that its surround.

and how can we paramelize it.

thanks very much

It is an example of a super ellipse, see here

RonL