MAT271H1 Study Guide - Midterm Guide: Leonhard Euler, Hypercube, Klein Bottle
Document Summary
Cube (cid:865) (cid:937) (cid:866) (cid:865) (cid:937) (cid:866) (cid:865) (cid:938) (cid:866) (cid:865) (cid:937) (cid:866) (cid:865) (cid:938) (cid:866) (cid:865) (cid:939) (cid:866) Hypercube (cid:865) (cid:937) (cid:866) (cid:865) (cid:938) (cid:866) (cid:865) (cid:939) (cid:866) (cid:865) (cid:936) (cid:866) Slice 3d shape into 2d sections, or a line in a plane w/ variable time. Slice 2d surfaces into lines e. g. topography, pressure maps, sections. Make 4d into 3d over time (aka. our universe) Mobius strip : 2d strip into a 3d tube, has only 1 side. Klein bottle in 4d, doesn"t cross over, cannot be done in 3d. Cutting klein bottle in half is 2 mobius strips. Perspective is like similar triangles, uses the same ratios. 1413 brunelleschi invented linear perspective ; many before him understood, tried but ultimately failed. Vanishing point is a point of infinity in mathematical terms; a direction which a family of parallel lines converge; there can be infinitely many.
