Anyonebrowsingatthestationerystorewillseeanincrediblearrayofpop-upcardsavailableforanyoccasion.Theworkingsofpop-upcardsandpop-upbookscanberemarkablyintricate.Behindsuchdesignsliesbeautifulgeometryinvolvingtheintersectionofcircles,cones,andspheres,themovementsoflinkages,andotherconstructions.Thegeometrycanbemodelledbyalgebraicequations,whosesolutionsexplainthedynamics.Forexample,severalpop-upmotionsrelyontheintersectionofthreespheres,acomputationmadeeverysecondforGPSlocation.Connectingthemotionsofthecardstructureswiththealgebraandgeometryrevealsabstractmathematicsperformingtangiblecalculations.Beginningwiththenephroidinthe19th-century,themathematicsofpop-updesignisnowatthefrontiersofrigidorigamiandalgorithmiccomputationalcomplexity.Alltopicsareaccessibletothosefamiliarwithhigh-schoolmathematics;nocalculusrequired.Explanationsaresupplementedby140+figuresand20animations.
