Introduction to Vector-Valued Functions

[@AmirJacob_94]

This is so cool!! Especially going from 3D to 2D by omitting an axis (the helix to cosine function blew my mind 😯)

[@ShahFahad-ez1cm]

You are Amazing. Words don't do justice to how good your explanation is.

[@DrClaireMath]

Thank you so much, this is very kind!

[@chickenfamily3711]

Nice explanation 🎉

[@DrClaireMath]

thank you!

[@legoweaponary1219]

Hey Claire, Im a mechanical engineer and have mathematical problem to solve. Imagine two given spheres anywhere in space with an equal radius. The intersection between them is a circle in space, but i want the curve in parametrized form. My solution is to make a new coordinate system with the origin in the center the circle. The z-axis is facing in the direction of the line between the two centers of the spheres. In this coordinate-system the equation of the circle is simple because the z-component is always zero. To get to this new coordinate system i first rotatet the original one around the z-axis and then around the new x-axis so it alines with the connection line. Then i get the solution by doing a coordinate-transformation, but the symbolic solution is very very long. My question is if you could think of a more elegent way of getting a closed symbolic parametrized solution of the intersection circle. Sadly my mathematical toolbox as a engineer is rather limited and i gues you coulf think of a nicer way to solve this problem. Greeting from Germany☺️

[@asmaazhar6460]

Very well explained.. Which software did you use for the visualisation of the curves?

[@DrClaireMath]

thank you! I used a website called Math3d: www.math3d.org/ I added it to the description too in case any one else is looking, thank you for your question! :)

[@nirmalaselvam5992]

@@DrClaireMath Thanks for the website. It's amazing. I did and I got the sin and cos graph but I didn't get the unit circle. Instead, I get a spiral. Why?

[@legendaryx2k19]

Wow , thank u

[@TheGibberingGoblin]

bump