0 4 Sc apmL<pKkW ,ebI KQ Q R Rֻ @{K ֻ  {   AKE 1999 UGA ֻ?*CFBC7ֻ1?.`wCC;3 ?2CCC>(6 {K89G  ,ebI TZZ[[p.sx͐.p.s  Evolute of Equiangular Spiraliral.PH|0|&̰p.0sx}kx}Hx͐.sx~ #}U<9}z4t ,ebI OQx۠t3]p _pt8 T HCCD  " ,ebI AQx۠t3s9p _pt8 T HAC  8 ,ebI MQx۠t3_p _pt8 T HD&CD c4  ,ebI SYYZZp؆ pD vPThe blue curve is an equiangular spiral. The red curve is its evolute, which can be generated as the envelope of its normals (red lines) or the locus of centers of its osculating circles (red dashed circles). An equiangular spiral's evolute is an identical equiangular spiral. Drag point D to change the constant angle of the spiral. Drag point K to adjust the position of point P on the curve. Drag point M to increase/decrease range of curves ploted. ۴0Հ۴pA ,ebI  AYYZZ8psx 8PsCCD " ,ebI  BCQx۠t3<p _pt8 T HAC#  B ,ebI  BQx۠t3qp _pt8 T HCC yT  ,ebI jH,@hx8K0 ;|d.x8K0} ; |d.x |CCDCCD? "Cx  ,ebI kxxK`8<|8|Cx8(Ag8bT:|c.|iN x8Kҕ`Tq>x~$x8KACB?55CCAC#A@l? ? ,ebI  KQx۠t3^5p _pt8 T HD1;CD AF?  ,ebI! DQx۠t3Sp _pt8 T HBkC) 0#<y ,ebI m2&8sxx$8T 6!@|.`8|` OK = |H4|DiⰂ|K`8` K5`|dx(ADD8BkC)AC?!5] ,ebI Animate 06sx 06soA++W` ,ebI#  p1!`xW<8X|"K`x<T|<8K`; <|ACB?S7CCBjC)A@l?=#I|T ,ebI m3`8.8 .xxx8K=xxx8K@xxx8   ln{(:AD}{!:*}tan{(:m{!:A}DBE} =