Parametric Calculus: Example 1: Involute of a Circle

in Threespeak2 months ago

▶️ Watch on 3Speak

In this video I go over an example on Calculus with Parametric Curves and this time describe the “involute” of a circle as a pair of Parametric Equations. The involute of a circle is the curve formed by tracing the path of the end of string as it is being unwound from the circle, while being held “taut”, or pulled tight so there is no slack. To determine the coordinates of the point on the involute curve, I show how we can use basic trigonometry to create two right-angle triangles, which we then can determine the coordinates by adding or subtracting the vertical or horizontal components. I also use the definition of arc length in establishing the length of the taut string in relation to the radius of the circle. This involute curve is a very interesting curve, and I will be using these derived parametric equations in my next video on the area of grazing a cow has so make sure to watch this video, and stay tuned for the next!

Download the notes in my video:!As32ynv0LoaIhvVm4-cIzzr8Xi4mFg

View video notes on the Hive blockchain:

Related Videos:

Parametric Calculus: Surface Area Part 1:

Parametric Calculus: Arc Length Part 1:

Parametric Calculus: Areas:

Parametric Calculus: Tangents:

Parametric Equations and Curves:

Angles - Degrees vs Radians: What are Radians??: .


DONATE! ʕ •ᴥ•ʔ

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

MES Truth:
Official Website:

MORE Links:

Email me: [email protected]

Free Calculators:

BMI Calculator:
Grade Calculator:
Mortgage Calculator:
Percentage Calculator:

Free Online Tools:

iPhone and Android Apps:

▶️ 3Speak


Hi, just informing You (and Your reader) that until 31th Octover one can invest in CCFound on Kanga Exchange, a Polish crypto exchange which does not require KYC (until You use only crypto without fiat). Here is link:

If You feel like that I am advertising that project too much, please tell me and I will stop. I dont want to embarass You. Best wishes.

Interesting. Thanks for the heads up. Looks like it's selling on Pancake Swap for $0.03 even with the slippage:

May grab some here.


PanCakeSwap liquidity was provided by some impatient investors from private sale who bought at 0.005$ and decided to sell before real launch in March 2022. If one buys more than 200-500$, price increases rapidly, some people who tried bought even at 0.07$. Secondly, if You buy on PCS You dont get airdrops.

Thirdly and most importantly, if You buy on PCS You support private sale investors, not CCFound Team.

Oh cool, thanks for the info! The airdrops could be important in the long run!

Hey @mes, sorry to jump in off-topic.
Do you mind reviewing and supporting the Hive Authentication Services proposal? That would be much appreciated.
Your feedback about the project is welcome too.
Thank you.

Cool cool. Just gave my support! Definitely a great idea.

Thank you for your support @mes, really appreciate it! 👍