Polygonal Spiral

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2020-03-16 18:49

This is an example of a polygonal spiral. It demonstrates the process of generating a spiral through rotation and distance transformation. Commands used include circle, line, intersect, rotate, distance, angle, and segment. Suitable for middle school and above students to learn about geometric transformations and spiral generation.

GeoGebra Commands & Parameters

Circle(P0, r0) → c0
Line(P0, P0_1) → s0
Intersect(c0, s0, 2) → P1
Circle(P1, Pc) → cP1
Intersect(cP1, s0, 2) → Be1
Circle(Be1, Pc) → cBe1
Intersect(cBe1, s0, 2) → Be2
Circle(P0, Be1) → ce1
Circle(Be2, Pc) → cBe2
Circle(P0, Be2) → ce2
Intersect(cBe2, s0, 2) → Be3
Circle(P0, Be3) → ce3
Circle(Be3, Pc) → cBe3
Intersect(cBe3, s0, 2) → Be4
Circle(Be4, Pc) → cBe4
Intersect(cBe4, s0, 2) → Be5
Circle(P0, Be5) → ce5
Circle(Be5, Pc) → cBe5
Intersect(cBe5, s0, 2) → Be6
Circle(Be6, Pc) → cBe6
Intersect(cBe6, s0, 2) → Be7
Circle(P0, Be7) → ce7
Circle(Be7, Pc) → cBe7
Intersect(cBe7, s0, 2) → Be8
Circle(Be8, Pc) → cBe8
Intersect(cBe8, s0, 2) → Be9
Circle(P0, Be9) → ce9
Circle(Be9, Pc) → cBe9
Intersect(cBe9, s0, 2) → Be10
Circle(Be10, Pc) → cBe10
Intersect(cBe10, s0, 2) → Be11
Circle(P0, Be11) → ce11
Circle(Be11, Pc) → cBe11
Intersect(cBe11, s0, 2) → Be12
Circle(Be12, Pc) → cBe12
Intersect(cBe12, s0, 2) → Be13
Circle(P0, Be13) → ce13
Circle(Be13, Pc) → cBe13
Intersect(cBe13, s0, 2) → Be14
Circle(Be14, Pc) → cBe14
Intersect(cBe14, s0, 2) → Be15
Circle(P0, Be15) → ce15
Circle(Be15, Pc) → cBe15
Intersect(cBe15, s0, 2) → Be16
Circle(Be16, Pc) → cBe16
Intersect(cBe16, s0, 2) → Be17
Circle(P0, Be17) → ce17
Circle(Be17, Pc) → cBe17
Intersect(cBe17, s0, 2) → Be18
Circle(Be18, Pc) → cBe18
Intersect(cBe18, s0, 2) → Be19
Circle(P0, Be19) → ce19
Circle(Be19, Pc) → cBe19
Intersect(cBe19, s0, 2) → Be20
Circle(Be20, Pc) → cBe20
Intersect(cBe20, s0, 2) → Be21
Circle(P0, Be21) → ce21
Circle(Be21, Pc) → cBe21
Intersect(cBe21, s0, 2) → Be22
Circle(Be22, Pc) → cBe22
Intersect(cBe22, s0, 2) → Be23
Circle(P0, Be23) → ce23
Circle(Be23, Pc) → cBe23
Intersect(cBe23, s0, 2) → Be24
Circle(Be24, Pc) → cBe24
Intersect(cBe24, s0, 2) → Be25
Circle(P0, Be25) → ce25
Circle(Be25, Pc) → cBe25
Intersect(cBe25, s0, 2) → Be26
Circle(Be26, Pc) → cBe26
Intersect(cBe26, s0, 2) → Be27
Circle(P0, Be27) → ce27
Circle(Be27, Pc) → cBe27
Intersect(cBe27, s0, 2) → Be28
Circle(Be28, Pc) → cBe28
Intersect(cBe28, s0, 2) → Be29
Circle(P0, Be29) → ce29
Circle(Be29, Pc) → cBe29
Intersect(cBe29, s0, 2) → Be30
Circle(Be30, Pc) → cBe30
Intersect(cBe30, s0, 2) → Be31
Circle(P0, Be31) → ce31
Circle(Be31, Pc) → cBe31
Intersect(cBe31, s0, 2) → Be32
Circle(Be32, Pc) → cBe32
Intersect(cBe32, s0, 2) → Be33
Circle(P0, Be33) → ce33
Circle(Be33, Pc) → cBe33
Intersect(cBe33, s0, 2) → Be34
Circle(Be34, Pc) → cBe34
Intersect(cBe34, s0, 2) → Be35
Circle(P0, Be35) → ce35
Circle(P0, Be34) → ce34
Circle(P0, Be32) → ce32
Circle(P0, Be30) → ce30
Circle(P0, Be28) → ce28
Circle(P0, Be26) → ce26
Circle(P0, Be24) → ce24
Circle(P0, Be22) → ce22
Circle(P0, Be20) → ce20
Circle(P0, Be18) → ce18
Circle(P0, Be16) → ce16
Circle(P0, Be14) → ce14
Circle(P0, Be12) → ce12
Circle(P0, Be10) → ce10
Circle(P0, Be8) → ce8
Circle(P0, Be6) → ce6
Circle(P0, Be4) → ce4
Rotate(P0_1, α, P1) → P1_1
Line(P1, P1_1) → rP1
Line(Be34, rP1) → rBe34
Intersect(ce35, rBe34, 2) → Fe34
Distance(Be34, Fe34) → De34
Intersect(ce1, rP1, 2) → We1
Angle(Be1, P0, We1) → εe1
Line(Be33, rP1) → rBe33
Intersect(ce34, rBe33, 2) → Fe33
Distance(Be33, Fe33) → De33
Line(Be32, rP1) → rBe32
Intersect(ce33, rBe32, 2) → Fe32
Distance(Be32, Fe32) → De32
Line(Be31, rP1) → rBe31
Intersect(ce32, rBe31, 2) → Fe31
Distance(Be31, Fe31) → De31
Line(Be30, rP1) → rBe30
Intersect(ce31, rBe30, 2) → Fe30
Distance(Be30, Fe30) → De30
Line(Be29, rP1) → rBe29
Intersect(ce30, rBe29, 2) → Fe29
Distance(Be29, Fe29) → De29
Line(Be28, rP1) → rBe28
Intersect(ce29, rBe28, 2) → Fe28
Distance(Be28, Fe28) → De28
Line(Be27, rP1) → rBe27
Intersect(ce28, rBe27, 2) → Fe27
Distance(Be27, Fe27) → De27
Line(Be26, rP1) → rBe26
Intersect(ce27, rBe26, 2) → Fe26
Distance(Be26, Fe26) → De26
Line(Be25, rP1) → rBe25
Intersect(ce26, rBe25, 2) → Fe25
Distance(Be25, Fe25) → De25
Line(Be24, rP1) → rBe24
Intersect(ce25, rBe24, 2) → Fe24
Distance(Be24, Fe24) → De24
Line(Be23, rP1) → rBe23
Intersect(ce24, rBe23, 2) → Fe23
Distance(Be23, Fe23) → De23
Line(Be22, rP1) → rBe22
Intersect(ce23, rBe22, 2) → Fe22
Distance(Be22, Fe22) → De22
Line(Be21, rP1) → rBe21
Intersect(ce22, rBe21, 2) → Fe21
Distance(Be21, Fe21) → De21
Line(Be20, rP1) → rBe20
Intersect(ce21, rBe20, 2) → Fe20
Distance(Be20, Fe20) → De20
Line(Be19, rP1) → rBe19
Intersect(ce20, rBe19, 2) → Fe19
Distance(Be19, Fe19) → De19
Line(Be18, rP1) → rBe18
Intersect(ce19, rBe18, 2) → Fe18
Distance(Be18, Fe18) → De18
Line(Be17, rP1) → rBe17
Intersect(ce18, rBe17, 2) → Fe17
Distance(Be17, Fe17) → De17
Line(Be16, rP1) → rBe16
Intersect(ce17, rBe16, 2) → Fe16
Distance(Be16, Fe16) → De16
Line(Be15, rP1) → rBe15
Intersect(ce16, rBe15, 2) → Fe15
Distance(Be15, Fe15) → De15
Line(Be14, rP1) → rBe14
Intersect(ce15, rBe14, 2) → Fe14
Distance(Be14, Fe14) → De14
Line(Be13, rP1) → rBe13
Intersect(ce14, rBe13, 2) → Fe13
Distance(Be13, Fe13) → De13
Line(Be12, rP1) → rBe12
Intersect(ce13, rBe12, 2) → Fe12
Distance(Be12, Fe12) → De12
Line(Be11, rP1) → rBe11
Intersect(ce12, rBe11, 2) → Fe11
Distance(Be11, Fe11) → De11
Line(Be10, rP1) → rBe10
Intersect(ce11, rBe10, 2) → Fe10
Distance(Be10, Fe10) → De10
Line(Be9, rP1) → rBe9
Intersect(ce10, rBe9, 2) → Fe9
Distance(Be9, Fe9) → De9
Line(Be8, rP1) → rBe8
Intersect(ce9, rBe8, 2) → Fe8
Distance(Be8, Fe8) → De8
Line(Be7, rP1) → rBe7
Intersect(ce8, rBe7, 2) → Fe7
Distance(Be7, Fe7) → De7
Line(Be6, rP1) → rBe6
Intersect(ce7, rBe6, 2) → Fe6
Distance(Be6, Fe6) → De6
Line(Be5, rP1) → rBe5
Intersect(ce6, rBe5, 2) → Fe5
Distance(Be5, Fe5) → De5
Line(Be4, rP1) → rBe4
Intersect(ce5, rBe4, 2) → Fe4
Distance(Be4, Fe4) → De4
Line(Be3, rP1) → rBe3
Intersect(ce4, rBe3, 2) → Fe3
Distance(Be3, Fe3) → De3
Line(Be2, rP1) → rBe2
Intersect(ce3, rBe2, 2) → Fe2
Distance(Be2, Fe2) → De2
Line(Be1, rP1) → rBe1
Intersect(ce2, rBe1, 2) → Fe1
Distance(Be1, Fe1) → De1
Rotate(Ke1, εe1 + α, We1) → We2
Angle(Be2, P0, We2) → εe2
Rotate(Ke2, εe2 + α, We2) → We3
Angle(Be3, P0, We3) → εe3
Rotate(Ke3, εe3 + α, We3) → We4
Angle(Be4, P0, We4) → εe4
Rotate(Ke4, εe4 + α, We4) → We5
Angle(Be5, P0, We5) → εe5
Rotate(Ke5, εe5 + α, We5) → We6
Angle(Be6, P0, We6) → εe6
Rotate(Ke6, εe6 + α, We6) → We7
Angle(Be7, P0, We7) → εe7
Rotate(Ke7, εe7 + α, We7) → We8
Angle(Be8, P0, We8) → εe8
Rotate(Ke8, εe8 + α, We8) → We9
Angle(Be9, P0, We9) → εe9
Rotate(Ke9, εe9 + α, We9) → We10
Angle(Be10, P0, We10) → εe10
Rotate(Ke10, εe10 + α, We10) → We11
Angle(Be11, P0, We11) → εe11
Rotate(Ke11, εe11 + α, We11) → We12
Angle(Be12, P0, We12) → εe12
Rotate(Ke12, εe12 + α, We12) → We13
Angle(Be13, P0, We13) → εe13
Rotate(Ke13, εe13 + α, We13) → We14
Angle(Be14, P0, We14) → εe14
Rotate(Ke14, εe14 + α, We14) → We15
Angle(Be15, P0, We15) → εe15
Rotate(Ke15, εe15 + α, We15) → We16
Angle(Be16, P0, We16) → εe16
Rotate(Ke16, εe16 + α, We16) → We17
Angle(Be17, P0, We17) → εe17
Rotate(Ke17, εe17 + α, We17) → We18
Angle(Be18, P0, We18) → εe18
Rotate(Ke18, εe18 + α, We18) → We19
Angle(Be19, P0, We19) → εe19
Rotate(Ke19, εe19 + α, We19) → We20
Angle(Be20, P0, We20) → εe20
Rotate(Ke20, εe20 + α, We20) → We21
Angle(Be20, P0, We21) → εe21
Rotate(Ke21, εe21 + α, We21) → We22
Angle(Be22, P0, We22) → εe22
Rotate(Ke22, εe22 + α, We22) → We23
Angle(Be23, P0, We23) → εe23
Rotate(Ke23, εe23 + α, We23) → We24
Angle(Be24, P0, We24) → εe24
Rotate(Ke24, εe24 + α, We24) → We25
Angle(Be25, P0, We25) → εe25
Rotate(Ke25, εe25 + α, We25) → We26
Angle(Be26, P0, We26) → εe26
Rotate(Ke26, εe26 + α, We26) → We27
Angle(Be27, P0, We27) → εe27
Rotate(Ke27, εe27 + α, We27) → We28
Angle(Be28, P0, We28) → εe28
Rotate(Ke28, εe28 + α, We28) → We29
Angle(Be29, P0, We29) → εe29
Rotate(Ke29, εe29 + α, We29) → We30
Angle(Be30, P0, We30) → εe30
Rotate(Ke30, εe30 + α, We30) → We31
Angle(Be31, P0, We31) → εe31
Rotate(Ke31, εe31 + α, We31) → We32
Angle(Be32, P0, We32) → εe32
Rotate(Ke32, εe32 + α, We32) → We33
Angle(Be33, P0, We33) → εe33
Rotate(Ke33, εe33 + α, We33) → We34
Angle(Be34, P0, We34) → εe34
Rotate(Ke34, εe34 + α, We34) → We35
Circle(Be35, Pc) → cBe35
Intersect(cBe35, s0, 2) → Be36
Circle(P0, Be36) → ce36
Line(Be35, rP1) → rBe35
Intersect(ce36, rBe35, 2) → Fe35
Segment(Be2, Fe2) → Spe3
Segment(Be3, Fe3) → Spe4
Segment(Be4, Fe4) → Spe5
Segment(Be5, Fe5) → Spe6
Segment(Be6, Fe6) → Spe7
Segment(Be7, Fe7) → Spe8
Segment(Be8, Fe8) → Spe9
Segment(Be9, Fe9) → Spe10
Segment(Be10, Fe10) → Spe11
Segment(Be11, Fe11) → Spe12
Segment(Be12, Fe12) → Spe13
Segment(Be13, Fe13) → Spe14
Segment(Be14, Fe14) → Spe15
Segment(Be15, Fe15) → Spe16
Segment(Be16, Fe16) → Spe17
Segment(Be17, Fe17) → Spe18
Segment(Be18, Fe18) → Spe19
Segment(Be19, Fe19) → Spe20
Segment(Be20, Fe20) → Spe21
Segment(Be21, Fe21) → Spe22
Segment(Be22, Fe22) → Spe23
Segment(Be23, Fe23) → Spe24
Segment(Be24, Fe24) → Spe25
Segment(Be25, Fe25) → Spe26
Segment(Be26, Fe26) → Spe27
Segment(Be27, Fe27) → Spe28
Segment(Be28, Fe28) → Spe29
Segment(Be29, Fe29) → Spe30
Segment(Be30, Fe30) → Spe31
Segment(Be31, Fe31) → Spe32
Segment(Be32, Fe32) → Spe33
Segment(Be33, Fe33) → Spe34
Segment(Be34, Fe34) → Spe35
Segment(Be35, Fe35) → Spe36
Segment(P1, We1) → SPpe1
Segment(Be1, Fe1) → Spe2
Distance(Be35, Fe35) → De35
Angle(Be35, P0, We35) → εe35
Rotate(Ke35, εe35 + α, We35) → We36
Segment(We1, We2) → SPpe2
Segment(We2, We3) → SPpe3
Segment(We3, We4) → SPpe4
Segment(We4, We5) → SPpe5
Segment(We5, We6) → SPpe6
Segment(We6, We7) → SPpe7
Segment(We7, We8) → SPpe8
Segment(We8, We9) → SPpe9
Segment(We9, We10) → SPpe10
Segment(We10, We11) → SPpe11
Segment(We11, We12) → SPpe12
Segment(We12, We13) → SPpe13
Segment(We13, We14) → SPpe14
Segment(We14, We15) → SPpe15
Segment(We15, We16) → SPpe16
Segment(We16, We17) → SPpe17
Segment(We17, We18) → SPpe18
Segment(We18, We19) → SPpe19
Segment(We19, We20) → SPpe20
Segment(We20, We21) → SPpe21
Segment(We21, We22) → SPpe22
Segment(We22, We23) → SPpe23
Segment(We23, We24) → SPpe24
Segment(We24, We25) → SPpe25
Segment(We25, We26) → SPpe26
Segment(We26, We27) → SPpe27
Segment(We27, We28) → SPpe28
Segment(We28, We29) → SPpe29
Segment(We29, We30) → SPpe30
Segment(We30, We31) → SPpe31
Segment(We31, We32) → SPpe32
Segment(We32, We33) → SPpe33
Segment(We33, We34) → SPpe34
Segment(We34, We35) → SPpe35
Segment(We35, We36) → SPpe36
Segment(P1, We1) → Spe1
Intersect(cP1, s0, 1) → Bi1
Line(Bi1, rP1) → rBi1
Circle(P0, Bi1) → ci1
Circle(Bi1, Pc) → cBi1
Intersect(cBi1, s0, 1) → Bi2
Circle(P0, Bi2) → ci2
Intersect(ci1, rP1, 1) → Wi1
Intersect(ci2, rBi1, 1) → Fi1
Segment(Bi1, Fi1) → Spi2
Line(Bi2, rP1) → rBi2
Circle(Bi2, Pc) → cBi2
Intersect(cBi2, s0, 1) → Bi3
Circle(P0, Bi3) → ci3
Intersect(ci3, rBi2, 1) → Fi2
Segment(Bi2, Fi2) → Spi3
Line(Bi3, rP1) → rBi3
Circle(Bi3, Pc) → cBi3
Intersect(cBi3, s0, 1) → Bi4
Circle(P0, Bi4) → ci4
Intersect(ci4, rBi3, 1) → Fi3
Segment(Bi3, Fi3) → Spi4
Line(Bi4, rP1) → rBi4
Circle(Bi4, Pc) → cBi4
Intersect(cBi4, s0, 1) → Bi5
Circle(P0, Bi5) → ci5
Intersect(ci5, rBi4, 1) → Fi4
Segment(Bi4, Fi4) → Spi5
Line(Bi5, rP1) → rBi5
Circle(Bi5, Pc) → cBi5
Intersect(cBi5, s0, 1) → Bi6
Circle(P0, Bi6) → ci6
Intersect(ci6, rBi5, 1) → Fi5
Segment(Bi5, Fi5) → Spi6
Line(Bi6, rP1) → rBi6
Circle(Bi6, Pc) → cBi6
Intersect(cBi6, s0, 1) → Bi7
Circle(P0, Bi7) → ci7
Intersect(ci7, rBi6, 1) → Fi6
Segment(Bi6, Fi6) → Spi7
Line(Bi7, rP1) → rBi7
Circle(Bi7, Pc) → cBi7
Intersect(cBi7, s0, 1) → Bi8
Circle(P0, Bi8) → ci8
Intersect(ci8, rBi7, 1) → Fi7
Segment(Bi7, Fi7) → Spi8
Segment(P1, Wi1) → SPpi1
Segment(P1, Wi1) → Spi1
Line(Bi8, rP1) → rBi8
Circle(Bi8, Pc) → cBi8
Intersect(cBi8, s0, 1) → Bi9
Circle(P0, Bi9) → ci9
Intersect(ci9, rBi8, 1) → Fi8
Segment(Bi8, Fi8) → Spi9
Line(Bi9, rP1) → rBi9
Circle(Bi9, Pc) → cBi9
Intersect(cBi9, s0, 1) → Bi10
Circle(P0, Bi10) → ci10
Intersect(ci10, rBi9, 1) → Fi9
Segment(Bi9, Fi9) → Spi10
Line(Bi10, rP1) → rBi10
Circle(Bi10, Pc) → cBi10
Intersect(cBi10, s0, 1) → Bi11
Circle(P0, Bi11) → ci11
Intersect(ci11, rBi10, 1) → Fi10
Segment(Bi10, Fi10) → Spi11
Line(Bi11, rP1) → rBi11
Circle(Bi11, Pc) → cBi11
Intersect(cBi11, s0, 1) → Bi12
Circle(P0, Bi12) → ci12
Intersect(ci12, rBi11, 1) → Fi11
Segment(Bi11, Fi11) → Spi12
Line(Bi12, rP1) → rBi12
Circle(Bi12, Pc) → cBi12
Intersect(cBi12, s0, 1) → Bi13
Circle(P0, Bi13) → ci13
Intersect(ci13, rBi12, 1) → Fi12
Segment(Bi12, Fi12) → Spi13
Line(Bi13, rP1) → rBi13
Circle(Bi13, Pc) → cBi13
Intersect(cBi13, s0, 1) → Bi14
Circle(P0, Bi14) → ci14
Intersect(ci14, rBi13, 1) → Fi13
Segment(Bi13, Fi13) → Spi14
Line(Bi14, rP1) → rBi14
Circle(Bi14, Pc) → cBi14
Intersect(cBi14, s0, 1) → Bi15
Circle(P0, Bi15) → ci15
Intersect(ci15, rBi14, 1) → Fi14
Segment(Bi14, Fi14) → Spi15
Line(Bi15, rP1) → rBi15
Circle(Bi15, Pc) → cBi15
Intersect(cBi15, s0, 1) → Bi16
Circle(P0, Bi16) → ci16
Intersect(ci16, rBi15, 1) → Fi15
Segment(Bi15, Fi15) → Spi16
Line(Bi16, rP1) → rBi16
Circle(Bi16, Pc) → cBi16
Intersect(cBi16, s0, 1) → Bi17
Circle(P0, Bi17) → ci17
Intersect(ci17, rBi16, 1) → Fi16
Segment(Bi16, Fi16) → Spi17
Line(Bi17, rP1) → rBi17
Circle(Bi17, Pc) → cBi17
Intersect(cBi17, s0, 1) → Bi18
Circle(P0, Bi18) → ci18
Intersect(ci18, rBi17, 1) → Fi17
Segment(Bi17, Fi17) → Spi18
Line(Bi18, rP1) → rBi18
Circle(Bi18, Pc) → cBi18
Intersect(cBi18, s0, 1) → Bi19
Circle(P0, Bi19) → ci19
Intersect(ci19, rBi18, 1) → Fi18
Segment(Bi18, Fi18) → Spi19
Line(Bi19, rP1) → rBi19
Circle(Bi19, Pc) → cBi19
Intersect(cBi19, s0, 1) → Bi20
Circle(P0, Bi20) → ci20
Intersect(ci20, rBi19, 1) → Fi19
Segment(Bi19, Fi19) → Spi20
Line(Bi20, rP1) → rBi20
Circle(Bi20, Pc) → cBi20
Intersect(cBi20, s0, 1) → Bi21
Circle(P0, Bi21) → ci21
Intersect(ci21, rBi20, 1) → Fi20
Segment(Bi20, Fi20) → Spi21
Line(Bi21, rP1) → rBi21
Circle(Bi21, Pc) → cBi21
Intersect(cBi21, s0, 1) → Bi22
Circle(P0, Bi22) → ci22
Intersect(ci22, rBi21, 1) → Fi21
Segment(Bi21, Fi21) → Spi22
Line(Bi22, rP1) → rBi22
Circle(Bi22, Pc) → cBi22
Intersect(cBi22, s0, 1) → Bi23
Circle(P0, Bi23) → ci23
Intersect(ci23, rBi22, 1) → Fi22
Segment(Bi22, Fi22) → Spi23
Line(Bi23, rP1) → rBi23
Circle(Bi23, Pc) → cBi23
Intersect(cBi23, s0, 1) → Bi24
Circle(P0, Bi24) → ci24
Intersect(ci24, rBi23, 1) → Fi23
Segment(Bi23, Fi23) → Spi24
Line(Bi24, rP1) → rBi24
Circle(Bi24, Pc) → cBi24
Intersect(cBi24, s0, 1) → Bi25
Circle(P0, Bi25) → ci25
Intersect(ci25, rBi24, 1) → Fi24
Segment(Bi24, Fi24) → Spi25
Line(Bi25, rP1) → rBi25
Circle(Bi25, Pc) → cBi25
Intersect(cBi25, s0, 1) → Bi26
Circle(P0, Bi26) → ci26
Intersect(ci26, rBi25, 1) → Fi25
Segment(Bi25, Fi25) → Spi26
Line(Bi26, rP1) → rBi26
Circle(Bi26, Pc) → cBi26
Intersect(cBi26, s0, 1) → Bi27
Circle(P0, Bi27) → ci27
Intersect(ci27, rBi26, 1) → Fi26
Segment(Bi26, Fi26) → Spi27
Line(Bi27, rP1) → rBi27
Circle(Bi27, Pc) → cBi27
Intersect(cBi27, s0, 1) → Bi28
Circle(P0, Bi28) → ci28
Intersect(ci28, rBi27, 1) → Fi27
Segment(Bi27, Fi27) → Spi28
Line(Bi28, rP1) → rBi28
Circle(Bi28, Pc) → cBi28
Intersect(cBi28, s0, 1) → Bi29
Circle(P0, Bi29) → ci29
Intersect(ci29, rBi28, 1) → Fi28
Segment(Bi28, Fi28) → Spi29
Line(Bi29, rP1) → rBi29
Circle(Bi29, Pc) → cBi29
Intersect(cBi29, s0, 1) → Bi30
Circle(P0, Bi30) → ci30
Intersect(ci30, rBi29, 1) → Fi29
Segment(Bi29, Fi29) → Spi30
Line(Bi30, rP1) → rBi30
Circle(Bi30, Pc) → cBi30
Intersect(cBi30, s0, 1) → Bi31
Circle(P0, Bi31) → ci31
Intersect(ci31, rBi30, 1) → Fi30
Segment(Bi30, Fi30) → Spi31
Line(Bi31, rP1) → rBi31
Circle(Bi31, Pc) → cBi31
Intersect(cBi31, s0, 1) → Bi32
Circle(P0, Bi32) → ci32
Intersect(ci32, rBi31, 1) → Fi31
Segment(Bi31, Fi31) → Spi32
Line(Bi32, rP1) → rBi32
Circle(Bi32, Pc) → cBi32
Intersect(cBi32, s0, 1) → Bi33
Circle(P0, Bi33) → ci33
Intersect(ci33, rBi32, 1) → Fi32
Segment(Bi32, Fi32) → Spi33
Line(Bi33, rP1) → rBi33
Circle(Bi33, Pc) → cBi33
Intersect(cBi33, s0, 1) → Bi34
Circle(P0, Bi34) → ci34
Intersect(ci34, rBi33, 1) → Fi33
Segment(Bi33, Fi33) → Spi34
Line(Bi34, rP1) → rBi34
Circle(Bi34, Pc) → cBi34
Intersect(cBi34, s0, 1) → Bi35
Circle(P0, Bi35) → ci35
Intersect(ci35, rBi34, 1) → Fi34
Segment(Bi34, Fi34) → Spi35
Line(Bi35, rP1) → rBi35
Circle(Bi35, Pc) → cBi35
Intersect(cBi35, s0, 1) → Bi36
Circle(P0, Bi36) → ci36
Intersect(ci36, rBi35, 1) → Fi35
Segment(Bi35, Fi35) → Spi36
Angle(Bi1, P0, Wi1) → εi1
Distance(Bi1, Fi1) → Di1
Distance(Bi2, Fi2) → Di2
Distance(Bi3, Fi3) → Di3
Distance(Bi4, Fi4) → Di4
Distance(Bi5, Fi5) → Di5
Distance(Bi6, Fi6) → Di6
Distance(Bi7, Fi7) → Di7
Distance(Bi8, Fi8) → Di8
Distance(Bi9, Fi9) → Di9
Distance(Bi10, Fi10) → Di10
Distance(Bi11, Fi11) → Di11
Distance(Bi12, Fi12) → Di12
Distance(Bi13, Fi13) → Di13
Distance(Bi14, Fi14) → Di14
Distance(Bi15, Fi15) → Di15
Distance(Bi16, Fi16) → Di16
Distance(Bi17, Fi17) → Di17
Distance(Bi18, Fi18) → Di18
Distance(Bi19, Fi19) → Di19
Distance(Bi20, Fi20) → Di20
Distance(Bi21, Fi21) → Di21
Distance(Bi22, Fi22) → Di22
Distance(Bi23, Fi23) → Di23
Distance(Bi24, Fi24) → Di24
Distance(Bi25, Fi25) → Di25
Distance(Bi26, Fi26) → Di26
Distance(Bi27, Fi27) → Di27
Distance(Bi28, Fi28) → Di28
Distance(Bi29, Fi29) → Di29
Distance(Bi30, Fi30) → Di30
Distance(Bi31, Fi31) → Di31
Distance(Bi32, Fi32) → Di32
Distance(Bi33, Fi33) → Di33
Distance(Bi34, Fi34) → Di34
Distance(Bi35, Fi35) → Di35
Rotate(Ki1, εi1 + α, Wi1) → Wi2
Angle(Bi2, P0, Wi2) → εi2
Rotate(Ki2, εi2 + α, Wi2) → Wi3
Angle(Bi3, P0, Wi3) → εi3
Rotate(Ki3, εi3 + α, Wi3) → Wi4
Angle(Bi4, P0, Wi4) → εi4
Rotate(Ki4, εi4 + α, Wi4) → Wi5
Angle(Bi5, P0, Wi5) → εi5
Rotate(Ki5, εi5 + α, Wi5) → Wi6
Angle(Bi6, P0, Wi6) → εi6
Rotate(Ki6, εi6 + α, Wi6) → Wi7
Angle(Bi7, P0, Wi7) → εi7
Rotate(Ki7, εi7 + α, Wi7) → Wi8
Angle(Bi8, P0, Wi8) → εi8
Rotate(Ki8, εi8 + α, Wi8) → Wi9
Angle(Bi9, P0, Wi9) → εi9
Rotate(Ki9, εi9 + α, Wi9) → Wi10
Angle(Bi10, P0, Wi10) → εi10
Rotate(Ki10, εi10 + α, Wi10) → Wi11
Angle(Bi11, P0, Wi11) → εi11
Rotate(Ki11, εi11 + α, Wi11) → Wi12
Angle(Bi12, P0, Wi12) → εi12
Rotate(Ki12, εi12 + α, Wi12) → Wi13
Angle(Bi13, P0, Wi13) → εi13
Rotate(Ki13, εi13 + α, Wi13) → Wi14
Angle(Bi14, P0, Wi14) → εi14
Rotate(Ki14, εi14 + α, Wi14) → Wi15
Angle(Bi15, P0, Wi15) → εi15
Rotate(Ki15, εi15 + α, Wi15) → Wi16
Angle(Bi16, P0, Wi16) → εi16
Rotate(Ki16, εi16 + α, Wi16) → Wi17
Angle(Bi17, P0, Wi17) → εi17
Rotate(Ki17, εi17 + α, Wi17) → Wi18
Angle(Bi18, P0, Wi18) → εi18
Rotate(Ki18, εi18 + α, Wi18) → Wi19
Angle(Bi19, P0, Wi19) → εi19
Rotate(Ki19, εi19 + α, Wi19) → Wi20
Angle(Bi20, P0, Wi20) → εi20
Rotate(Ki20, εi20 + α, Wi20) → Wi21
Angle(Bi21, P0, Wi21) → εi21
Rotate(Ki21, εi21 + α, Wi21) → Wi22
Angle(Bi22, P0, Wi22) → εi22
Rotate(Ki22, εi22 + α, Wi22) → Wi23
Angle(Bi23, P0, Wi23) → εi23
Rotate(Ki23, εi23 + α, Wi23) → Wi24
Angle(Bi24, P0, Wi24) → εi24
Rotate(Ki24, εi24 + α, Wi24) → Wi25
Angle(Bi25, P0, Wi25) → εi25
Rotate(Ki25, εi25 + α, Wi25) → Wi26
Angle(Bi26, P0, Wi26) → εi26
Rotate(Ki26, εi26 + α, Wi26) → Wi27
Angle(Bi27, P0, Wi27) → εi27
Rotate(Ki27, εi27 + α, Wi27) → Wi28
Angle(Bi28, P0, Wi28) → εi28
Rotate(Ki28, εi28 + α, Wi28) → Wi29
Angle(Bi29, P0, Wi29) → εi29
Rotate(Ki29, εi29 + α, Wi29) → Wi30
Angle(Bi30, P0, Wi30) → εi30
Rotate(Ki30, εi30 + α, Wi30) → Wi31
Angle(Bi31, P0, Wi31) → εi31
Rotate(Ki31, εi31 + α, Wi31) → Wi32
Angle(Bi32, P0, Wi32) → εi32
Rotate(Ki32, εi32 + α, Wi32) → Wi33
Angle(Bi33, P0, Wi33) → εi33
Rotate(Ki33, εi33 + α, Wi33) → Wi34
Angle(Bi34, P0, Wi34) → εi34
Rotate(Ki34, εi34 + α, Wi34) → Wi35
Angle(Bi35, P0, Wi35) → εi35
Rotate(Ki35, εi35 + α, Wi35) → Wi36
Segment(Wi1, Wi2) → SPpi2
Segment(Wi2, Wi3) → SPpi3
Segment(Wi3, Wi4) → SPpi4
Segment(Wi4, Wi5) → SPpi5
Segment(Wi5, Wi6) → SPpi6
Segment(Wi6, Wi7) → SPpi7
Segment(Wi7, Wi8) → SPpi8
Segment(Wi8, Wi9) → SPpi9
Segment(Wi9, Wi10) → SPpi10
Segment(Wi10, Wi11) → SPpi11
Segment(Wi11, Wi12) → SPpi12
Segment(Wi12, Wi13) → SPpi13
Segment(Wi13, Wi14) → SPpi14
Segment(Wi14, Wi15) → SPpi15
Segment(Wi15, Wi16) → SPpi16
Segment(Wi16, Wi17) → SPpi17
Segment(Wi17, Wi18) → SPpi18
Segment(Wi18, Wi19) → SPpi19
Segment(Wi19, Wi20) → SPpi20
Segment(Wi20, Wi21) → SPpi21
Segment(Wi21, Wi22) → SPpi22
Segment(Wi22, Wi23) → SPpi23
Segment(Wi23, Wi24) → SPpi24
Segment(Wi24, Wi25) → SPpi25
Segment(Wi25, Wi26) → SPpi26
Segment(Wi26, Wi27) → SPpi27
Segment(Wi27, Wi28) → SPpi28
Segment(Wi28, Wi29) → SPpi29
Segment(Wi29, Wi30) → SPpi30
Segment(Wi30, Wi31) → SPpi31
Segment(Wi31, Wi32) → SPpi32
Segment(Wi32, Wi33) → SPpi33
Segment(Wi33, Wi34) → SPpi34
Segment(Wi34, Wi35) → SPpi35
Segment(Wi35, Wi36) → SPpi36