{"version":10,"randomSeed":"e52a18431a74a70e6aefe0380d119c7a","graph":{"viewport":{"xmin":-3.9697496029281676,"ymin":-1.6217373535197517,"xmax":2.7462258275902873,"ymax":3.5494157748653743},"product":"geometry-calculator"},"expressions":{"list":[{"type":"folder","id":"**dcg_geo_folder**","title":"geometry","secret":true},{"type":"expression","id":"1","color":"#c74440","latex":"f\\left(s\\right)=f_{2}\\left(s\\right)"},{"type":"expression","id":"54","color":"#c74440","latex":"f_{1}\\left(t\\right)=\\left(t,0.6\\sin13.2t+0.2\\sin23.3t+0.05\\cos87.3t\\right)"},{"type":"expression","id":"55","color":"#2d70b3","latex":"f_{2}\\left(t\\right)=\\left(t,\\frac{\\cos8t}{t^{2}+1}\\right)","hidden":true},{"type":"expression","id":"56","color":"#388c46","latex":"f_{3}\\left(t\\right)=\\left(\\cos\\left(t\\right)+0.1\\cos\\left(4t\\right),\\sin\\left(t\\right)+0.1\\sin\\left(4t\\right)\\right)"},{"type":"expression","id":"64","color":"#000000","latex":"f\\left(t\\right)","parametricDomain":{"min":"-5","max":"5"},"domain":{"min":"-5","max":"5"}},{"type":"expression","id":"12","color":"#000000","latex":"p_1=\\left(-1.17,1.67\\right)"},{"type":"expression","id":"13","color":"#000000","latex":"p_2=\\left(-2.774,1.1\\right)"},{"type":"expression","id":"9","color":"#6042a6","latex":"F\\left(t\\right)=\\operatorname{distance}\\left(p_{1},f\\left(t\\right)\\right)+\\operatorname{distance}\\left(p_{2},f\\left(t\\right)\\right)","hidden":true},{"type":"expression","id":"31","color":"#000000","latex":"K=\\left[2...1000\\right]"},{"type":"expression","id":"32","color":"#c74440","latex":"X=\\left[-5,-4.99,...5\\right]"},{"type":"expression","id":"33","color":"#2d70b3","latex":"R=X\\left[\\left\\{F\\left(X\\left[K+1\\right]\\right)>F\\left(X\\left[K\\right]\\right)\\right\\}\\left\\{F\\left(X\\left[K-1\\right]\\right)>F\\left(X\\left[K\\right]\\right)\\right\\}=1\\right]"},{"type":"expression","id":"35","color":"#6042a6","latex":"R_{c}=\\operatorname{sort}\\left(R,\\operatorname{distance}\\left(p_{1},f\\left(R\\right)\\right)+\\operatorname{distance}\\left(p_{2},f\\left(R\\right)\\right)\\right)\\left[1...5\\right]"},{"type":"expression","id":"29","color":"#fa7e19","latex":"\\left[\\operatorname{segment}\\left(p_{1},f\\left(x_{1}\\right)\\right)\\operatorname{for}x_{1}=R_{c}\\right]","lineOpacity":"1"},{"type":"expression","id":"36","color":"#6042a6","latex":"\\left[\\operatorname{segment}\\left(p_{2},f\\left(x_{1}\\right)\\right)\\operatorname{for}x_{1}=R_{c}\\right]"},{"type":"expression","id":"40","color":"#2d70b3","latex":"N\\left(t\\right)=-\\frac{\\frac{\\left(\\frac{d}{dt}f\\left(t+h\\right)\\right)}{\\operatorname{distance}\\left(\\left(0,0\\right),\\frac{d}{dt}f\\left(t+h\\right)\\right)}-\\frac{\\left(\\frac{d}{dt}f\\left(t-h\\right)\\right)}{\\operatorname{distance}\\left(\\left(0,0\\right),\\frac{d}{dt}f\\left(t-h\\right)\\right)}}{2h}"},{"type":"expression","id":"43","color":"#000000","latex":"h=0.001","hidden":true,"slider":{"hardMin":true,"hardMax":true,"min":"0","max":"1"}},{"type":"expression","id":"37","color":"#c74440","latex":"\\left[\\operatorname{segment}\\left(f\\left(x_{1}\\right),f\\left(x_{1}\\right)+N\\left(x_{1}\\right)\\right)\\operatorname{for}x_{1}=R_{c}\\right]","hidden":true},{"type":"expression","id":"51","color":"#fa7e19","latex":"\\left[\\operatorname{angle}\\left(p_{1},f\\left(x_{1}\\right),f\\left(x_{1}\\right)+N\\left(x_{1}\\right)\\right)\\operatorname{for}x_{1}=R_{c}\\right]"},{"type":"expression","id":"53","color":"#6042a6","latex":"\\left[\\operatorname{angle}\\left(p_{2},f\\left(x_{1}\\right),f\\left(x_{1}\\right)+N\\left(x_{1}\\right)\\right)\\operatorname{for}x_{1}=R_{c}\\right]"}]}}