▁phenomen on ▁of ▁points ▁and ▁sets ▁of ▁singular ities ▁is ▁studied , ▁as ▁part ▁of ▁the ▁concept ▁that ▁manif olds ▁( spaces ▁without ▁singular ities ) ▁may ▁ac quire ▁special , ▁singular ▁points ▁by ▁a ▁number ▁of ▁routes . ▁Pro jection ▁is ▁one ▁way , ▁very ▁obvious ▁in ▁visual ▁terms ▁when ▁three - dimensional ▁objects ▁are ▁project ed ▁into ▁two ▁dimensions ▁( for ▁example ▁in ▁one ▁of ▁our ▁eyes ); ▁in ▁looking ▁at ▁classical ▁stat u ary ▁the ▁fol ds ▁of ▁dra per y ▁are ▁amongst ▁the ▁most ▁obvious ▁features . ▁Sing ular ities ▁of ▁this ▁kind ▁include ▁ca ust ics , ▁very ▁familiar ▁as ▁the ▁light ▁patterns ▁at ▁the ▁bottom ▁of ▁a ▁sw imming ▁pool . ▁ ▁Other ▁ways ▁in ▁which ▁singular ities ▁occur ▁is ▁by ▁deg ener ation ▁of ▁manifold ▁structure . ▁The ▁presence ▁of ▁symmetry ▁can ▁be ▁good ▁cause ▁to ▁consider ▁orb if olds , ▁which ▁are ▁manif olds ▁that ▁have ▁acquired ▁" c orn ers " ▁in ▁a ▁process ▁of ▁fol ding ▁up , ▁res emb ling ▁the ▁cre asing ▁of ▁a ▁table ▁nap kin . ▁ ▁Sing ular ities ▁in ▁algebraic ▁geometry ▁ ▁Al gebra ic ▁curve ▁singular ities ▁ ▁Histor ically , ▁singular ities ▁were ▁first ▁noticed ▁in ▁the ▁study ▁of ▁algebraic ▁curves . ▁The ▁double ▁point ▁at ▁( 0 ,   0 ) ▁of ▁the ▁curve ▁ ▁and ▁the ▁c us p ▁there ▁of ▁ ▁are ▁qual it atively ▁different , ▁as ▁is ▁seen ▁just ▁by ▁sketch ing . ▁Isaac ▁Newton ▁carried ▁out ▁a ▁detailed ▁study