Pensieve header: Plotting a saddle and a torus for January 27.

1617-257 Fri Jan 27, hour 46: Manifolds and boundaries, integration on manifolds.

Read Along. Sections 24-25.

Riddle Along. The game of 15 is played as follows. Two players alternate choosing cards numbered between 1 and 9, with repetitions forbidden, so the game ends at most after 9 moves (or 4(1/2) rounds). The first player to have within their cards a set of precisely 3 cards that add up to 15 wins. Would you rather move first or second?

Anyone looks good (from some angle)

ParametricPlot3D[
{x,y,(x^2)-(y^2)},
{x,-1,1}, {y,-1,1},
PlotStyle ->Opacity[0.5],
ViewPoint->{5,5,0}, ViewVertical->{0,0,1}
]

ParametricPlot3D[
{Cos[α](2+Cos[β]),Sin[α](2+Cos[β]),Sin[β]},
{α,0,2π}, {β,0,2π},
PlotStyle ->Opacity[0.5],
ViewPoint->{5,5,0}, ViewVertical->{0,0,1}
]