chain-frac-0.tcl
transform a real number into a chain fraction
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ad_page_contract { transform a real number into a chain fraction } -query { x } set page "" append page "<html> <body> <h2>Chain Fraction</h2>" set e [expr {exp(1)}] set e0 [expr {int ( $e ) }]; # keep the integer part in e0 set xf [expr {1 / ($e - $e0) }]; # invert the fractional part set e1 [expr {int ( $xf ) }]; # keep the integer part in e1 set xf [expr {1 / ($xf - $e1) }]; # invert the fractional part set e2 [expr {int ( $xf ) }]; # keep the integer part in e2 set xf [expr {1 / ($xf - $e2) }]; # invert the fractional part set e3 [expr {int ( $xf ) }]; # keep the integer part in e3 set xf [expr {1 / ($xf - $e3) }]; # invert the fractional part set e4 [expr {int ( $xf ) }]; # keep the integer part in e4 set xf [expr {1 / ($xf - $e4) }]; # invert the fractional part set e5 [expr {int ( $xf ) }]; # keep the integer part in e5 set xf [expr {1 / ($xf - $e5) }]; # invert the fractional part set e6 [expr {int ( $xf ) }]; # keep the integer part in e6 set xf [expr {1 / ($xf - $e6) }]; # invert the fractional part set e7 [expr {int ( $xf ) }]; # keep the integer part in e7 set xf [expr {1 / ($xf - $e7) }]; # invert the fractional part set e8 [expr {int ( $xf ) }]; # keep the integer part in e8 set xf [expr {1 / ($xf - $e8) }]; # invert the fractional part set e9 [expr {int ( $xf ) }]; # keep the integer part in e9 set xf [expr {1 / ($xf - $e9) }]; # invert the fractional part set e10 [expr {int ( $xf ) }]; # keep the integer part in e10 set xf [expr {1 / ($xf - $e10) }]; # invert the fractional part set e11 [expr {int ( $xf ) }]; # keep the integer part in e11 set xf [expr {1 / ($xf - $e11) }]; # invert the fractional part set e12 [expr {int ( $xf ) }]; # keep the integer part in e12 set xf [expr {1 / ($xf - $e12) }]; # invert the fractional part set e13 [expr {int ( $xf ) }]; # keep the integer part in e13 set xf [expr {1 / ($xf - $e13) }]; # invert the fractional part set e14 [expr {int ( $xf ) }]; # keep the integer part in e14 set xf [expr {1 / ($xf - $e14) }]; # invert the fractional part set e15 [expr {int ( $xf ) }]; # keep the integer part in e15 set xf [expr {1 / ($xf - $e15) }]; # invert the fractional part set e16 [expr {int ( $xf ) }]; # keep the integer part in e16 set xf [expr {1 / ($xf - $e16) }]; # invert the fractional part set e17 [expr {int ( $xf ) }]; # keep the integer part in e17 set xf [expr {1 / ($xf - $e17) }]; # invert the fractional part set e18 [expr {int ( $xf ) }]; # keep the integer part in e18 set xf [expr {1 / ($xf - $e18) }]; # invert the fractional part set e19 [expr {int ( $xf ) }]; # keep the integer part in e19 set xf [expr {1 / ($xf - $e19) }]; # invert the fractional part append page " <h3>Natural <var>e</var></h3> <p> $e = $e0 + 1/( $e1 + 1/( $e2 + 1/( $e3 + 1/( $e4 + 1/( $e5 + 1/( $e6 + 1/( $e7 + 1/( $e8 + 1/( $e9 + 1/( $e10 + 1/( $e11 + 1/( $e12 + 1/( $e13 + 1/( $e14 + 1/( $e15 + 1/( $e16 + 1/( $e17 + 1/( $e18 + 1/( $e19 + ... ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) </p>" # golden ratio set g [expr (sqrt(5)+1)/2] set g0 [expr {int ( $g ) }]; # keep the integer part in g0 set xf [expr {1 / ($g - $g0) }]; # invert the fractional part set g1 [expr {int ( $xf ) }]; # keep the integer part in g1 set xf [expr {1 / ($xf - $g1) }]; # invert the fractional part set g2 [expr {int ( $xf ) }]; # keep the integer part in g2 set xf [expr {1 / ($xf - $g2) }]; # invert the fractional part set g3 [expr {int ( $xf ) }]; # keep the integer part in g3 set xf [expr {1 / ($xf - $g3) }]; # invert the fractional part set g4 [expr {int ( $xf ) }]; # keep the integer part in g4 set xf [expr {1 / ($xf - $g4) }]; # invert the fractional part set g5 [expr {int ( $xf ) }]; # keep the integer part in g5 set xf [expr {1 / ($xf - $g5) }]; # invert the fractional part set g6 [expr {int ( $xf ) }]; # keep the integer part in g6 set xf [expr {1 / ($xf - $g6) }]; # invert the fractional part set g7 [expr {int ( $xf ) }]; # keep the integer part in g7 set xf [expr {1 / ($xf - $g7) }]; # invert the fractional part set g8 [expr {int ( $xf ) }]; # keep the integer part in g8 set xf [expr {1 / ($xf - $g8) }]; # invert the fractional part set g9 [expr {int ( $xf ) }]; # keep the integer part in g9 set xf [expr {1 / ($xf - $g9) }]; # invert the fractional part set g10 [expr {int ( $xf ) }]; # keep the integer part in g10 set xf [expr {1 / ($xf - $g10) }]; # invert the fractional part set g11 [expr {int ( $xf ) }]; # keep the integer part in g11 set xf [expr {1 / ($xf - $g11) }]; # invert the fractional part set g12 [expr {int ( $xf ) }]; # keep the integer part in g12 set xf [expr {1 / ($xf - $g12) }]; # invert the fractional part set g13 [expr {int ( $xf ) }]; # keep the integer part in g13 set xf [expr {1 / ($xf - $g13) }]; # invert the fractional part set g14 [expr {int ( $xf ) }]; # keep the integer part in g14 set xf [expr {1 / ($xf - $g14) }]; # invert the fractional part set g15 [expr {int ( $xf ) }]; # keep the integer part in g15 set xf [expr {1 / ($xf - $g15) }]; # invert the fractional part set g16 [expr {int ( $xf ) }]; # keep the integer part in g16 set xf [expr {1 / ($xf - $g16) }]; # invert the fractional part set g17 [expr {int ( $xf ) }]; # keep the integer part in g17 set xf [expr {1 / ($xf - $g17) }]; # invert the fractional part set g18 [expr {int ( $xf ) }]; # keep the integer part in g18 set xf [expr {1 / ($xf - $g18) }]; # invert the fractional part set g19 [expr {int ( $xf ) }]; # keep the integer part in g19 set xf [expr {1 / ($xf - $g19) }]; # invert the fractional part append page " <h3>Golden Ratio</h3> <p> $g = $g0 + 1/( $g1 + 1/( $g2 + 1/( $g3 + 1/( $g4 + 1/( $g5 + 1/( $g6 + 1/( $g7 + 1/( $g8 + 1/( $g9 + 1/( $g10 + 1/( $g11 + 1/( $g12 + 1/( $g13 + 1/( $g14 + 1/( $g15 + 1/( $g16 + 1/( $g17 + 1/( $g18 + 1/( $g19 + ... ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) </p>" # Square root of 3 set r [expr {sqrt(3)}] set r0 [expr {int ( $r ) }]; # keep the integer part in r0 set xf [expr {1 / ($r - $r0) }]; # invert the fractional part set r1 [expr {int ( $xf ) }]; # keep the integer part in r1 set xf [expr {1 / ($xf - $r1) }]; # invert the fractional part set r2 [expr {int ( $xf ) }]; # keep the integer part in r2 set xf [expr {1 / ($xf - $r2) }]; # invert the fractional part set r3 [expr {int ( $xf ) }]; # keep the integer part in r3 set xf [expr {1 / ($xf - $r3) }]; # invert the fractional part set r4 [expr {int ( $xf ) }]; # keep the integer part in r4 set xf [expr {1 / ($xf - $r4) }]; # invert the fractional part set r5 [expr {int ( $xf ) }]; # keep the integer part in r5 set xf [expr {1 / ($xf - $r5) }]; # invert the fractional part set r6 [expr {int ( $xf ) }]; # keep the integer part in r6 set xf [expr {1 / ($xf - $r6) }]; # invert the fractional part set r7 [expr {int ( $xf ) }]; # keep the integer part in r7 set xf [expr {1 / ($xf - $r7) }]; # invert the fractional part set r8 [expr {int ( $xf ) }]; # keep the integer part in r8 set xf [expr {1 / ($xf - $r8) }]; # invert the fractional part set r9 [expr {int ( $xf ) }]; # keep the integer part in r9 set xf [expr {1 / ($xf - $r9) }]; # invert the fractional part set r10 [expr {int ( $xf ) }]; # keep the integer part in r10 set xf [expr {1 / ($xf - $r10) }]; # invert the fractional part set r11 [expr {int ( $xf ) }]; # keep the integer part in r11 set xf [expr {1 / ($xf - $r11) }]; # invert the fractional part set r12 [expr {int ( $xf ) }]; # keep the integer part in r12 set xf [expr {1 / ($xf - $r12) }]; # invert the fractional part set r13 [expr {int ( $xf ) }]; # keep the integer part in r13 set xf [expr {1 / ($xf - $r13) }]; # invert the fractional part set r14 [expr {int ( $xf ) }]; # keep the integer part in r14 set xf [expr {1 / ($xf - $r14) }]; # invert the fractional part set r15 [expr {int ( $xf ) }]; # keep the integer part in r15 set xf [expr {1 / ($xf - $r15) }]; # invert the fractional part set r16 [expr {int ( $xf ) }]; # keep the integer part in r16 set xf [expr {1 / ($xf - $r16) }]; # invert the fractional part set r17 [expr {int ( $xf ) }]; # keep the integer part in r17 set xf [expr {1 / ($xf - $r17) }]; # invert the fractional part set r18 [expr {int ( $xf ) }]; # keep the integer part in r18 set xf [expr {1 / ($xf - $r18) }]; # invert the fractional part set r19 [expr {int ( $xf ) }]; # keep the integer part in r19 set xf [expr {1 / ($xf - $r19) }]; # invert the fractional part append page " <h3>Square root of 3</h3> <p> $r = $r0 + 1/( $r1 + 1/( $r2 + 1/( $r3 + 1/( $r4 + 1/( $r5 + 1/( $r6 + 1/( $r7 + 1/( $r8 + 1/( $r9 + 1/( $r10 + 1/( $r11 + 1/( $r12 + 1/( $r13 + 1/( $r14 + 1/( $r15 + 1/( $r16 + 1/( $r17 + 1/( $r18 + 1/( $r19 + ... ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) </p>" # the user's x set n0 [expr {int ( $x ) }]; # keep the integer part in n0 set xf [expr {1 / ($x - $n0) }]; # invert the fractional part set n1 [expr {int ( $xf ) }]; # keep the integer part in n1 set xf [expr {1 / ($xf - $n1) }]; # invert the fractional part set n2 [expr {int ( $xf ) }]; # keep the integer part in n2 set xf [expr {1 / ($xf - $n2) }]; # invert the fractional part set n3 [expr {int ( $xf ) }]; # keep the integer part in n3 set xf [expr {1 / ($xf - $n3) }]; # invert the fractional part set n4 [expr {int ( $xf ) }]; # keep the integer part in n4 set xf [expr {1 / ($xf - $n4) }]; # invert the fractional part set n5 [expr {int ( $xf ) }]; # keep the integer part in n5 set xf [expr {1 / ($xf - $n5) }]; # invert the fractional part set n6 [expr {int ( $xf ) }]; # keep the integer part in n6 set xf [expr {1 / ($xf - $n6) }]; # invert the fractional part set n7 [expr {int ( $xf ) }]; # keep the integer part in n7 set xf [expr {1 / ($xf - $n7) }]; # invert the fractional part set n8 [expr {int ( $xf ) }]; # keep the integer part in n8 set xf [expr {1 / ($xf - $n8) }]; # invert the fractional part set n9 [expr {int ( $xf ) }]; # keep the integer part in n9 set xf [expr {1 / ($xf - $n9) }]; # invert the fractional part set n10 [expr {int ( $xf ) }]; # keep the integer part in n10 set xf [expr {1 / ($xf - $n10) }]; # invert the fractional part set n11 [expr {int ( $xf ) }]; # keep the integer part in n11 set xf [expr {1 / ($xf - $n11) }]; # invert the fractional part set n12 [expr {int ( $xf ) }]; # keep the integer part in n12 set xf [expr {1 / ($xf - $n12) }]; # invert the fractional part set n13 [expr {int ( $xf ) }]; # keep the integer part in n13 set xf [expr {1 / ($xf - $n13) }]; # invert the fractional part set n14 [expr {int ( $xf ) }]; # keep the integer part in n14 set xf [expr {1 / ($xf - $n14) }]; # invert the fractional part set n15 [expr {int ( $xf ) }]; # keep the integer part in n15 set xf [expr {1 / ($xf - $n15) }]; # invert the fractional part set n16 [expr {int ( $xf ) }]; # keep the integer part in n16 set xf [expr {1 / ($xf - $n16) }]; # invert the fractional part set n17 [expr {int ( $xf ) }]; # keep the integer part in n17 set xf [expr {1 / ($xf - $n17) }]; # invert the fractional part set n18 [expr {int ( $xf ) }]; # keep the integer part in n18 set xf [expr {1 / ($xf - $n18) }]; # invert the fractional part set n19 [expr {int ( $xf ) }]; # keep the integer part in n19 set xf [expr {1 / ($xf - $n19) }]; # invert the fractional part append page " <h3>Your <var>x</var></h3> <p> $x = $n0 + 1/( $n1 + 1/( $n2 + 1/( $n3 + 1/( $n4 + 1/( $n5 + 1/( $n6 + 1/( $n7 + 1/( $n8 + 1/( $n9 + 1/( $n10 + 1/( $n11 + 1/( $n12 + 1/( $n13 + 1/( $n14 + 1/( $n15 + 1/( $n16 + 1/( $n17 + 1/( $n18 + 1/( $n19 + ... ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) </p> </body> </html> " doc_return 200 text/html $page # Local variables: # mode: tcl # tcl-indent-level: 4 # indent-tabs-mode: nil # End:
