Running Circles Around Circles: Part 1: Hypocycloid Proof скачать в хорошем качестве

Running Circles Around Circles: Part 1: Hypocycloid Proof

In this video go over a very interesting Laboratory Project, which is a cool math project at the end of some of the chapters in my Calculus book, and the project I go over is called Running Circles Around Circles. This project looks at the curves generated by, just as the title states, a point on a circle that rotates around another circle, either on the inside or outside of that circle. In part 1 of the project I derive the parametric equations for the curve generated when the circle is rotating INSIDE of the other circle. The resulting curve is called a hypocycloid. Rotating on the outside is called a epicycloid, and which I will go over this in later parts of this video series. In this derivation, I show how we can use basic geometric and trigonometry to determine equations for the coordinates of the point on the circle we are tracing. This is a great video into the crazy and fascinating world of the types of parametric curves that can be sketched and formulated, so make sure to watch this video! Also stay tuned for future parts of this laboratory project because some of the curves are truly amazing! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuEAY... View Video Notes on Steemit: https://steemit.com/mathematics/@mes/... Related Videos: Parametric Curves: Superellipses:    • Parametric Curves: Superellipses   Parametric Curves: Example 11: Conchoids of Nicomedes:    • Parametric Curves: Example 11: Conchoids o...   Parametric Curves: Example 7: The Cycloid: Proof Part 1:    • Parametric Curves: Example 7: The Cycloid:...   Parametric Curves: Example 6: Graphing Devices:    • Parametric Curves: Example 6: Graphing Dev...   Parametric Curves: Example 5: Lissajous Figure:    • Parametric Curves: Example 5: Lissajous Fi...   Parametric Equations and Curves:    • Parametric Equations and Curves   Parametric Equations and Polar Coordinates:    • Parametric Equations and Polar Coordinates   Angles - Degrees vs Radians: What are Radians??:    • Angles - Degrees vs Radians: What are Radi...   Trigonometry: Sine, Cosine and Tan Functions:    • Trigonometry: Sine, Cosine and Tan Functions   . ------------------------------------------------------ Become a MES Super Fan!    / @mes   DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps