6 ms·
No. As soon as you have 4 points, these 4 points uniquely define a cubic. Even if those 4 points are "right next" to eachother. If this is difficult to imagin
by lucas-beyer 14y ago
No.
As soon as you have 4 points, these 4 points uniquely define a cubic. Even if those 4 points are "right next" to eachother.
If this is difficult to imagine, it is the same with a line. Wherever you place 2 points, they always uniquely define a single line.
Unless, of course, you place 2 points exactly on top of eachother.
- xk_id 14y agoreally? that's amazing! I'd love to see a formal proof of this. edit: I suppose this counts as proof http://www.had2know.com/academics/cubic-through-4-points.html http://www.had2know.com/academics/cubic-through-4-points.htm..., but atm I don't remember why matrixes are connected with equations.
- joshzayin 14y agoThere's a more general proof at https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:nm.mathforcollege.com/mws/gen/05inp/mws_gen_inp_bck_introduction.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESg6HcId-jvRg7Ihh3dMF3DGTmBUCUOukBjCH1SunBJxGZFV3gri-zWyN91qUSinDMFJ3lvexKfgAvN3xewN2mWfG6idDKfHutuAcb62pH-UHJJXLUnbo3dCjt12NyTTYiZHuqDR&sig=AHIEtbSO9AURkaDNywKJ62dsSWklsecAEw https://docs.google.com/viewer?a=v&q=cache:euFgQLUCTfwJ:... that looks reasonable at a skim.
- xk_id 14y agoAwesome!