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3blue1brown's profile
Grant Sanderson
Grant Sanderson
Grant Sanderson
@3blue1brown

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Grant Sanderson

@3blue1brown

Animated videos about math: http://www.3blue1brown.com 

3blue1brown.com
Joined October 2014

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    Grant Sanderson‏ @3blue1brown 10 Jul 2018

    Draw many lines from an arbitrary point in a circle to its circumference. Rotate each by 90 degrees around its center. What emerges is a perfect ellipse. Can you prove why?pic.twitter.com/nlxAfjjowy

    11:44 pm - 10 Jul 2018
    • 196 Retweets
    • 831 Likes
    • John Sweeney LeMuhr On Sports Bacrima Max Solberg yoyocliche Alexy Khrabrov [AKA Dr. Like Duh] Brendan W. Sullivan Daniel Bhatti Malcolm Hafely
    29 replies . 196 retweets 831 likes
      1. New conversation
      2. Grant Sanderson‏ @3blue1brown 10 Jul 2018

        More lines!pic.twitter.com/BF5ASBBoeX

        2 replies . 18 retweets 159 likes
        Show this thread
      3. Grant Sanderson‏ @3blue1brown 10 Jul 2018

        Hint: There are really only two special points in this diagram, the center of the circle, and the point from which all the lines emerge. Two special points. Ellipse. Hmmm...

        11 replies . 5 retweets 132 likes
        Show this thread
      4. End of conversation
      1. New conversation
      2. Scott Farrar‏ @farrarscott 11 Jul 2018
        Replying to @3blue1brown

        Play here: https://www.geogebra.org/m/rgtfeswh  What happens outside?pic.twitter.com/BkBzUUh6wH

        5 replies . 12 retweets 140 likes
      3. Grant Sanderson‏ @3blue1brown 11 Jul 2018
        Replying to @farrarscott

        Extend the lines some more, and I believe you get a hyperbola.

        2 replies . 0 retweets 20 likes
      4. Gustavo BC‏ @_Gustavobc 11 Jul 2018
        Replying to @3blue1brown @farrarscott

        So do you get a parabola when B is right on the circumference?

        3 replies . 0 retweets 1 like
      5. Gustavo BC‏ @_Gustavobc 11 Jul 2018
        Replying to @_Gustavobc @3blue1brown @farrarscott

        Update: I tried and honestly I can't make any conclusions from thispic.twitter.com/fc1E7L96j2

        1 reply . 1 retweet 7 likes
      6. Grant Sanderson‏ @3blue1brown 11 Jul 2018
        Replying to @_Gustavobc @farrarscott

        Let the line extend much more.

        1 reply . 0 retweets 3 likes
      7. Gustavo BC‏ @_Gustavobc 11 Jul 2018
        Replying to @3blue1brown @farrarscott

        Changed "Segment" in the code to "Line", set B to exactly (1,0), but I'm still not sure what I'm seeing here. Looks the same even zooming all the way in. The Moirés are neat thoughpic.twitter.com/H00nYP7Dce

        1 reply . 0 retweets 3 likes
      8. 3 more replies
      1. New conversation
      2. A_Lampshade2278‏ @lampshade2278 11 Jul 2018
        Replying to @3blue1brown

        Is this a hint as to what the next video is about???

        1 reply . 0 retweets 1 like
      3. Grant Sanderson‏ @3blue1brown 11 Jul 2018
        Replying to @lampshade2278

        😉

        1 reply . 0 retweets 3 likes
      4. A_Lampshade2278‏ @lampshade2278 11 Jul 2018
        Replying to @3blue1brown

        u slick boi 😁

        0 replies . 0 retweets 4 likes
      5. End of conversation
      1. New conversation
      2. MKoot‏ @_MKoot 10 Jul 2018
        Replying to @3blue1brown

        A definition of an ellipse is equal distances from a cirkel to a point within the circle. So when you take lines from the point to the circle and flip them by their centre they have equal distances and since it’s 90 degrees they are tangent to the elipse.

        1 reply . 0 retweets 11 likes
      3. MKoot‏ @_MKoot 11 Jul 2018
        Replying to @_MKoot @3blue1brown

        Sorry, autocorrect turned circle to cirkel (which is Dutch for circle)

        2 replies . 0 retweets 3 likes
      4. Dr Salman A‏ @muSALMANia 11 Jul 2018
        Replying to @_MKoot @3blue1brown

        Exactly how circle sounds in English!

        0 replies . 0 retweets 12 likes
      5. End of conversation
      1. New conversation
      2. MKoot‏ @_MKoot 11 Jul 2018
        Replying to @_MKoot @3blue1brown

        An ellipse has equal distances from the (focal) point to a circle. If you draw a line from the point to the circle and create a perpendicular bisector, you ensure that every point on the bisector has an equal distance. 1/2

        1 reply . 0 retweets 0 likes
      3. MKoot‏ @_MKoot 11 Jul 2018
        Replying to @_MKoot @3blue1brown

        Then you just have to draw a line from the center to the point on the circle and repeat that process for each point on the circle… and there you have it. A beautiful ellipse. 2/2

        0 replies . 0 retweets 0 likes
      4. End of conversation
      1. Neil Gunther‏ @DrQz 11 Jul 2018
        Replying to @3blue1brown

        Hodographic mapping. The orthogonal lines can be thought of as incremental velocities. Greatest change is at the perihelion.

        0 replies . 0 retweets 5 likes
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