A Hyperbolic Paraboloid Can Be Generated by Straight lines

avatar

▶️ Watch on 3Speak

In this video I show that a hyperbolic paraboloid can be generated entirely by two sets of lines, thus classifying it as a Ruled Surface. The only quadric surfaces that are ruled surfaces are cylinders, cones, and hyperboloids of one sheet. All of these can be generated by the motion of straight lines. A hyperbolic paraboloid has horizontal traces that are hyperbolas and vertical traces that are parabolas. I show that two sets of lines in parametric equations can be plugged directly into the equation of the hyperboloid paraboloid and obtain a point on it. I also play around with the lines using GeoGebra's 3D graphing calculator to show that the lines are always on the hyperbolic paraboloid, which is pretty amazing when you think about it!

GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec

Time stamps:

  • Exercise 2: Hyperbolic Paraboloid Generated from Lines: 0:00
  • Ruled Surfaces: hyperbolic paraboloids, cylinders, cones, hyperboloids of one sheet: 0:41
  • Solution: Recall equation of a hyperbolic paraboloid: 1:30
  • Recall parametric equations of a line: 2:49
  • Plugging in first line equation into hyperboloid paraboloid: 4:00
  • Plugging in second line equation: 7:01
  • Two sets of lines on the hyperboloid paraboloid in vector form: 9:46
  • Graphing in GeoGebra: 12:01

Full video below:

  • Cylinders and Quadric Surfaces:
  • HIVE video notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
  • Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
  • Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

    • Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

    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

    ▶️ 3Speak

    math geometry science stemgeeks stemsocial palnet proofofbrain chessbrothers freecompliments stem education
    0
    0
    0.000
    2 comments
    avatar

    Congratulations @mes! You have completed the following achievement on the Hive blockchain And have been rewarded with New badge(s)

    You received more than 15000 HP as payout for your posts, comments and curation.
    Your next payout target is 16000 HP.
    The unit is Hive Power equivalent because post and comment rewards can be split into HP and HBD

    You can view your badges on your board and compare yourself to others in the Ranking
    If you no longer want to receive notifications, reply to this comment with the word STOP

    0
    0
    0.000
    Reply