perm filename PAGE93[0,BGB] blob
sn#115982 filedate 1974-08-16 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00005 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00002 00002 {≤GP93W0,750,100,1900λ25JUFA}
C00004 00003 L560,700C5I∂10,∂20}L{I∂0,∂-120}≤a≥{L560-320,690}a{
C00006 00004 L400,-300C160C5
C00007 00005 L400,-700C160,-150*π/180,300*π/180C5
C00008 ENDMK
C⊗;
{≤G;P93;W0,750,100,1900;λ25;JUFA}
\In order to put the iron triangle
into the tripod, the edge BC is first placed
between the tripod legs of angle ≤a≥. Let
a be the length of BC, likewise b and c
are the lengths of AC and AB.
\Restricting attention to the plane LBC,
consider the locus of points L' arrived at
by sliding the tripod and maintaining
contacts at B and C.
\Remembering that in a circle, a chord
subtends equal angles at all points of each
arc on either side of the chord; it can be seen
that the set of possible L' points lie
on a circular arc. Let this arc be called L's arc, which is part of L's
circle.
\Also in a circle the angle at the center
is double the angle at the
circumference, when the rays forming the
angles meet the circumference in the
same two points.
\And the perpendicular bisector of a
chord passes thru the center of the
chord's circle bisecting the central
angle. Let S be the distance between the
center of the circle and the chord BC.
So by trigonometric definitions:
{JC} R = a / 2sin(≤a≥)
{JC} S = R cos(≤a≥)
{H3;
L560,700;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-320,690;}a{
L560,700,560-350,700+94;
L560,700,560-350,700-94;
L560,700;C50,165*π/180,30*π/180;
L400-138,700+80;C5;I∂-10,∂-5;}B{
L400-138,700-80;C5;I∂30,∂-5;}C{
L400-138,700+80,400-138,700-80;
L560,400;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-320,390;}a{
L560,400,560-350,400+94;
L560,400,560-350,400-94;
L560,400;C50,165*π/180,30*π/180;
L400-138,400+80;C5;I∂-10,∂-5;}B{
L400-138,400-80;C5;I∂30,∂-5;}C{
L400-138,400+80,400-138,400-80;
L502,522;C5;I∂0,∂10;}L'{
L502-70,522-35;}≤a≥{
L502,522;C50,190*π/180,30*π/180;
L502,522,502-345,522-60;
L502,522,502-268,522-225;
L560,100;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-315,90;}a{
L560,100,560-350,100+94;
L560,100,560-350,100-94;
L560,100;C50,165*π/180,30*π/180;
L400-138,100+80;C5;I∂-10,∂-10;}B{
L400-138,100-80;C5;I∂30,∂-10;}C{
L400-138,100+80,400-138,100-80;
L502,222;C5;I∂0,∂10;}L'{
L502-70,222-35;}≤a≥{
L502,222;C50,190*π/180,30*π/180;
L502,222,502-345,222-60;
L502,222,502-268,222-225;
L400,100;C160;
L400,-300;C160;C5;
C50,150*π/180,60*π/180;I∂10,∂-90;}2≤a≥{
L400,-300,400-138,-300+80;
L400,-300,400-138,-300-80;
L560,-300;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-315,-310;}a{
L560,-300,560-350,-300+94;
L560,-300,560-350,-300-94;
L560,-300;C50,165*π/180,30*π/180;
L400-138,-300+80;C5;I∂-10,∂-10;}B{
L400-138,-300-80;C5;I∂30,∂-10;}C{
L400-138,-300+80,400-138,-300-80;
L400,-700;C160,-150*π/180,300*π/180;C5;
L400-80,-700-30;}S{
L400-80,-700+50;}R{
L400-190,-700+25;}a/2{
L400,-700;
C50,150*π/180,30*π/180;I∂-10,∂-75;}≤a≥{
L400-138,-700+80;C5;I∂-10,∂-10;}B{
L400-138,-700-80;C5;I∂30,∂-10;}C{
L400-138,-700-80,400-138,-700+80,400,-700;
L400-138,-700,400+160,-700;
W0,1260,100,1800;λ30}