GSP4„¾»è†QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$èñßLHalf-Plane Model` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H±Arial ±Geneva"³³ ³'''$'ÿ$'€$'€$'ÿÿ$'€€$'€$'ÃÃ$'ÿÿÿ$'   $' $' $' %'&'8'8'8'9':'ÐÿÕþÿP[2]Ø™H„@x@×ÐÿÕïÿP[1]Ø™A@x@×ÐDüüD1><0>>Õ˜nÁQ\aAt[1]ؘ•z×Ð? € Ò×é‡è†QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$èóLCredits` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H ±Geneva"³ '''$'mtr$'nme$' fj$'€€$'€€$'€$'ÃÃ$'ÿÿÿ$'   $' $' $' %'&'8'8'8'9':'Ð$üü$0Ð>ؘ0Ðaã×ÐDüüB/º.>)¤Ø˜/ºÍ×Ð h  h »Lhttp://www.keypress.com/sketchpad/general_resources/advanced_sketch_gallery/P0Õ˜nÁQ\aAAdvanced Sketch GalleryØ¢»³Î×Ð <  < bÐ!http://www.keypress.com/sketchpad2Õ˜nÁQ\aASketchpad Resource CenterØ¢bÐã×Ðüü$4ï<0><0><0><0>>ؘ$4 ¡×é‡ö†V{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êLHalf-plane Segment±Arial ±Geneva"³³ÐÕ˜nÁQ\aABØ™tnvescam×ÐÕ˜nÁQ\aAAØ™þÿÿÿ×ÐÕ˜nÁQ\aAP[2]Ø™L€{5×ÐÕ˜nÁQ\aAP[1]Ø™À"ÀŠ×Ð Ò×Ð?  Ò×Ð ÿÿÿÒÕ˜nÁQ\aAFØ×Ð/ ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿ ÒÕ˜nÁQ\aAEØ×Ð Ò ×Ð -ÿÿÿ Ò Õ˜nÁQ\aADØ×Ð -ÿÿÿ Ò Õ˜nÁQ\aACØ×ÐO CÒ ×Ð -ÀÀ Ò Õ˜nÁQ\aABØ×Ð -ÿÿÿ Ò Õ˜nÁQ\aAAØ×ÐQ CÀÀÒ×ÐQ CÀÀÒ×´¸/#Hyperbolic Segment Segments in the half-plane model are (Euclidean) arcs of semi-circles orthogonal to the border. This tool constructs a half-plane segment between points A and B.ë‡ö†V{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ê LHalf-plane Line±Arial ±Geneva"³³ÐÕ˜nÁQ\aAP[2]Ø™×ÐÕ˜nÁQ\aAP[1]Ø™ÐI!0 þ×ÐÕ˜nÁQ\aABØ™@C¦C˜A×ÐÕ˜nÁQ\aAAØ™×Ð Ò×Ð ÿÿÿÒÕ˜nÁQ\aADØ×Ð/ ÒÕ˜nÁQ\aAjØ×Ð?  Ò×Ð -ÿÿÿ ÒÕ˜nÁQ\aACØ×Ð Ò ×Ð -ÿÿÿ Ò Õ˜nÁQ\aAAØ×Ð -ÿÿÿ Ò Õ˜nÁQ\aABØ×ÐO CÿÒ ×´®/#Hyperbolic Line Lines in the half-plane model are (Euclidean) semi-circles orthogonal to the border line. This tool constructs a non-Euclidean line through points A and B. ë‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êLHalf-plane Distance±Arial ±Geneva"³³³ ÐÕ˜nÁQ\aAP[2]Ø™€ ê»Iû×ÐÕ˜nÁQ\aAP[1]Ø™ ¹×ÐÕ˜nÁQ\aABØ™{5×ÐÕ˜nÁQ\aAAØ™þÿÿÿ×Ð Ò×Ð?  Ò×Ð ÿÿÿÒÕ˜nÁQ\aADØ×Ð/ ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿ ÒÕ˜nÁQ\aACØ×Ð Ò ×Ð -ÿÿÿ Ò Õ˜nÁQ\aAAØ×Ð -ÿÿÿ Ò Õ˜nÁQ\aABØ×Ð%0 Ò  ü6<0>Ø×Ð%0 Ò  ü)<0>dàØ×Ð%0 Ò  ü<0>Ø×Ð%0 Ò  ü<0>dàØ×Ð0 !Ò z üC<0>»:/ Z0 ``  `` Õ˜nÁQ\aAm[1]Ø×Ð0 !Òd üz<0>»:/ D0`8Õ=hyperbolic distance {3} to {4}Ø×´Z/#Hyperbolic Distance A and B are two points in the hyperbolic plane (half-plane model). ë‡ö†V{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êLHalf-plane Angle±Arial ±Geneva"³³³ ÐÕ˜nÁQ\aAP[2]Ø™€l{0í×ÐÕ˜nÁQ\aAP[1]Ø™þÿÿÿ×ÐÕBØ™×ÐÕ˜nÁQ\aAAØ™ЬÒ×ÐÕ˜nÁQ\aACØ™€?×Ð Ò×Ð Ò×Ð?  Ò×Ð ÿÿÿÒÕ˜nÁQ\aAFØ×Ð ÿÿÿÒÕ˜nÁQ\aAEØ×Ð/ Ò Õ˜nÁQ\aAoØ×Ð/ Ò Õ˜nÁQ\aAnØ×Ð -ÿÿÿ Ò Õ˜nÁQ\aADØ×Ð -ÿÿÿ Ò Õ˜nÁQ\aACØ×Ð Ò ×Ð Ò×Ð/ ÒÕ˜nÁQ\aAmØ×Ð/ ÒÕ˜nÁQ\aAkØ×Ð/ ÒÕ˜nÁQ\aAlØ×Ð/ ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿ ÒÕ˜nÁQ\aABØ×Ð -ÿÿÿ ÒÕ˜nÁQ\aAAØ×Ð)1Ò  ü‡<0>6Õ˜nÁQ\aA=hyperbolic angle {3}-{4}-{5}Ø×´„/#Hyperbolic Angle This tool constructs the measure of the half-plane angle determined by points A, B, and C, with B as the vertex.o뇅