# cusp math definition

cusp math definition - A simple cusp is a point on a curve where the curve crosses itself, and where the two branches of the curve share a common tangent, the branches being on opposite sides of the tangent.

Basically its the point on the curve that turns back on itself. It looks symmetrical and the point on the curve where the branches meet share a common tangent point. This would be where the red point is on the graph below. The branches are also on opposite sides of the tangent.

For example, this plot shows the curve of y²=x³ which is a semicubical parabola.

Sometimes they are also called vertical cusps because they look like it is going double back on itself. In this case the graph is infinite. However, not all graphs are infinite that show signs of a cusp.

This is a not a cusp

Related words: Tangent, plot, graph, semi

There are many ways to donating. One way is, if you found this helpful please pass it along by sharing it with your friends. I am sure they would really appreciate your insight into the wonderful world of cusps!

'Like' this site?

Return from Cusp Math Definition to Math Glossary

Return from Cusp Math Definition to Math Problem Solving

Find a Math Word here

Can't find the word you are looking for? Do a search here and type your word in the box below

Good, better best.

Never, ever rest.

Like this website?

"I am getting much better test marks and I have been moved up a set"
Sumera
Age 13
England

"High school's great, I'm in a good math set and I understand lots of things, thanks to you"
Eleanor Talbot
Age 11
England

"I really like math now, you just make it more friendly and normal"
Jess Johnson
Age 18
England

"Your writing style is great, informative but friendly! My 12 year old son still struggles with basic maths. I can see your website will be a real treasure trove for us :)"
Jackie
New Zealand