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apply assume Axiom bounded Chapter choose circle claim classes closed collection complete composition compute congruent conjugate consider construction containing coordinate corresponding define Definition denote described desired determine directed angle measure distance distinct equal equation equivalent established Euclidean example Exercise exists fact finite fixed point formula four frieze groups geometry given gives glide reflection Hence Hint implies important interior intersect invariant isometry lattice length line segment maps means obtain opposite orbit original pair parallel parallelogram particular patterns perpendicular plane point group polygonal regions positive possible preserves proof properties Proposition Prove radius real number reflection result rotation shown in Figure side similarity split square Structure subgroup Suppose symmetry group Theorem transformations translation triangle union unique verify vertices
Seite xiii - That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 4 - the best way to explain it is to do it." (And, as you might like to try the thing yourself some winter day, I will tell you how the Dodo managed it.) First it marked out a race-course, in a sort of circle, ("the exact shape doesn't matter," it said,) and then all the party were placed along the course, here and there. There was no "One, two...