The FIRST of the seven beauties! The integral of the unit tangent over a curve.

[@theoremus]

The closed curve looks like a Maxwell Equation for magnetism - beautiful.

[@tomholroyd7519]

This is beautiful

[@MathTheBeautiful]

Thank you, agreed!

[@sindreabrahamsen4286]

When do we get the full course series?

[@JBerry00]

Thank you!

[@MathTheBeautiful]

Glad you enjoyed it!

[@nickhardy7310]

If only you had been my teacher many years ago!

[@MathTheBeautiful]

The night is young!

[@queenslayerthefifth1771]

What happened if it's not the unit tangent vector?

[@MathTheBeautiful]

Then it would be a different result. What kind of tangent vector would you like to integrate?

[@queenslayerthefifth1771]

@MathTheBeautiful I was thinking about just the tangent vector without it being of unit length. Will this then just be a scalar multiple of the result we get from the same operation using the unit tangent vector?

[@MathTheBeautiful]

The answer would very much depend on how you decide to specify the variable length of the tangent vector.

[@queenslayerthefifth1771]

@MathTheBeautiful I see. I will think about it a.little more.I appreciate you taking the time to answer .

[@Pluralist]

[@alegian7934]

i was expecting some kind of proof, but it all happened so easily

[@MathTheBeautiful]

Yes!