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έναρξη

ανενεργό

περιστροφή (ανενεργό)

διαδρομή

Σε κάθε γραμμή, στήλη και διαγώνιο το άθροισμα θα είναι : 

Μαγικά τετράγωνα ονομάζουμε αυτά που το άθροισμα των αριθμών
σε κάθε γραμμή, σε κάθε στήλη και σε κάθε διαγώνιο είναι ίσα. 

Βοήθεια 1

Βοήθεια 2

                           Ο πρώτος και μικρότερος αριθμός, από την ομάδα των αριθμών
που θα τοποθετηθούν στο “Μαγικό” τετράγωνο.

Πρώτος (m) :

Βήμα (b) :

Κατά πόσο θα αυξάνονται ή μειώνονται οι αριθμοί της ομάδας.

★ Μετακινήστε τους δρομείς για να αλλάξουν οι αριθμοί που αντιπροσωπεύουν

- Zoom +  :

Αυξάνει ή μειώνει το μέγεθος του τετραγώνου

K

περιστροφή

Μόνος μου

ΜΑΓΙΚΑ ΤΕΤΡΑΓΩΝΑ ΠΕΡΙΤΤΗΣ ΤΑΞΗΣ

e1 = false
t = 0 (slider from 0 to n2, step 0.01)
n = 1 (slider from 1 to 7, step 2)
r1 = 3 (slider from 2.5 to 5, step 0.1)
K = (2.8377383592017664, -0.17680709534367933)
c = Circle(K, r1)
d: y = x + y(K) - x(K)
AA = Intersect(c, d, 1)
t2 = 0 (slider from 0 to 4, step 0.01)
A1 = Rotate(AA, ((-((t2 * 90))))°, K)
ε01 = Line(K, A1)
A3 = Intersect(c, ε01, 2)
ε02 = OrthogonalLine(K, ε01)
A4, A2 = Intersect(c, ε02)
λίστα3 = ΔιαίρεσηΤμήματοςΣεΙσαμέρη(A4, A3, (2 * n))
λίστα2 = ΔιαίρεσηΤμήματοςΣεΙσαμέρη(A3, A2, (2 * n))
λίστα4 = ΔιαίρεσηΤμήματοςΣεΙσαμέρη(A1, A2, (2 * n))
Ka2 = Segment(Element[λίστα3, 3], Element[λίστα4, 3])
λίστα1 = ΔιαίρεσηΤμήματοςΣεΙσαμέρη(A4, A1, (2 * n))
Or1 = Segment(Element[λίστα1, 1], Element[λίστα2, 1])
T12 = Intersect(Ka2, Or1)
Or7 = Segment(Element[λίστα1, 13], Element[λίστα2, 13])
Or4 = Segment(Element[λίστα1, 7], Element[λίστα2, 7])
Or5 = Segment(Element[λίστα1, 9], Element[λίστα2, 9])
Ka7 = Segment(Element[λίστα3, 13], Element[λίστα4, 13])
T57 = Intersect(Or5, Ka7)
Ka1 = Segment(Element[λίστα3, 1], Element[λίστα4, 1])
T41 = Intersect(Or4, Ka1)
Ka5 = Segment(Element[λίστα3, 9], Element[λίστα4, 9])
T75 = Intersect(Or7, Ka5)
ε26 = Line(T57, T75)
T45 = Intersect(Or4, Ka5)
ε04 = Line(T45, T41)
Ka4 = Segment(Element[λίστα3, 7], Element[λίστα4, 7])
T55 = Intersect(Or5, Ka5)
T15 = Intersect(Or1, Ka5)
ε03 = Line(T15, T55)
T14 = Intersect(Or1, Ka4)
ε25 = Line(T14, T41)
b = 1 (slider from -15 to 15, step 1)
m = 1 (slider from -10 to 20, step 1)
Ar = Sequence(i, i, m, m + ((n^(2) - 1) * b), b)
Ar1 = If(n > 0, Take[Ar, 1, If[n ≤ 3, n^(2), 25]], {})
Ar2 = If(n > 5, Take[Ar, 26, 49], {})
KK1 = TableText({Ar1, Ar2}, "Hc_|")
ArK = Sequence(ToBase[i, 10], i, m, m + ((n^(2) - 1) * b), b)
K01 = Element(ArK, 1)
K02 = Element(ArK, 2)
K03 = Element(ArK, 3)
K04 = Element(ArK, 4)
K05 = Element(ArK, 5)
K06 = Element(ArK, 6)
K07 = Element(ArK, 7)
K08 = Element(ArK, 8)
K09 = Element(ArK, 9)
K10 = Element(ArK, 10)
K11 = Element(ArK, 11)
K12 = Element(ArK, 12)
K13 = Element(ArK, 13)
K14 = Element(ArK, 14)
K15 = Element(ArK, 15)
K16 = Element(ArK, 16)
K17 = Element(ArK, 17)
K18 = Element(ArK, 18)
K19 = Element(ArK, 19)
K20 = Element(ArK, 20)
K21 = Element(ArK, 21)
K22 = Element(ArK, 22)
K23 = Element(ArK, 23)
K24 = Element(ArK, 24)
K25 = Element(ArK, 25)
K26 = Element(ArK, 26)
K27 = Element(ArK, 27)
K28 = Element(ArK, 28)
K29 = Element(ArK, 29)
K30 = Element(ArK, 30)
K31 = Element(ArK, 31)
K32 = Element(ArK, 32)
K33 = Element(ArK, 33)
K34 = Element(ArK, 34)
K35 = Element(ArK, 35)
K36 = Element(ArK, 36)
K37 = Element(ArK, 37)
K38 = Element(ArK, 38)
K39 = Element(ArK, 39)
K40 = Element(ArK, 40)
K41 = Element(ArK, 41)
K42 = Element(ArK, 42)
K43 = Element(ArK, 43)
K44 = Element(ArK, 44)
K45 = Element(ArK, 45)
K46 = Element(ArK, 46)
K47 = Element(ArK, 47)
K48 = Element(ArK, 48)
K49 = Element(ArK, 49)
Or2 = Segment(Element[λίστα1, 3], Element[λίστα2, 3])
Or3 = Segment(Element[λίστα1, 5], Element[λίστα2, 5])
Or6 = Segment(Element[λίστα1, 11], Element[λίστα2, 11])
Ka3 = Segment(Element[λίστα3, 5], Element[λίστα4, 5])
Ka6 = Segment(Element[λίστα3, 11], Element[λίστα4, 11])
T11 = Intersect(Or1, Ka1)
T13 = Intersect(Or1, Ka3)
T16 = Intersect(Or1, Ka6)
T17 = Intersect(Or1, Ka7)
T21 = Intersect(Or2, Ka1)
T22 = Intersect(Or2, Ka2)
T23 = Intersect(Or2, Ka3)
T24 = Intersect(Or2, Ka4)
T25 = Intersect(Or2, Ka5)
T26 = Intersect(Or2, Ka6)
T27 = Intersect(Or2, Ka7)
T31 = Intersect(Or3, Ka1)
T32 = Intersect(Or3, Ka2)
T33 = Intersect(Or3, Ka3)
T34 = Intersect(Or3, Ka4)
T35 = Intersect(Or3, Ka5)
T36 = Intersect(Or3, Ka6)
T37 = Intersect(Or3, Ka7)
T47 = Intersect(Or4, Ka7)
T46 = Intersect(Or4, Ka6)
T44 = Intersect(Or4, Ka4)
T43 = Intersect(Or4, Ka3)
T42 = Intersect(Or4, Ka2)
T51 = Intersect(Or5, Ka1)
T52 = Intersect(Or5, Ka2)
T53 = Intersect(Or5, Ka3)
T54 = Intersect(Or5, Ka4)
T56 = Intersect(Or5, Ka6)
T67 = Intersect(Or6, Ka7)
T66 = Intersect(Or6, Ka6)
T65 = Intersect(Or6, Ka5)
T64 = Intersect(Or6, Ka4)
T63 = Intersect(Or6, Ka3)
T62 = Intersect(Or6, Ka2)
T61 = Intersect(Or6, Ka1)
T71 = Intersect(Or7, Ka1)
T72 = Intersect(Or7, Ka2)
T73 = Intersect(Or7, Ka3)
T74 = Intersect(Or7, Ka4)
T76 = Intersect(Or7, Ka6)
T77 = Intersect(Or7, Ka7)
T05 = Intersect(ε03, ε25)
uT14a = Vector(T14, T05)
uT14b = Vector(T05, T75)
v2 = false
t1 = 0 (slider from 0 to 1, step 0.01)
v1 = false
Q775 = Κίνηση2(t - 3, T75, T66, T66)
Q766 = Κίνηση2(t - 4, T66, T57, T57)
T40 = Intersect(ε26, ε04)
uT75a = Vector(T75, T40)
uT75b = Vector(T40, T41)
Q757 = Κίνηση2(t - 5, T57, T40, T41)
uT41 = Vector(T41, T23)
Q741 = Κίνηση2(t - 7, T41, T32, T32)
Q732 = Κίνηση2(t - 8, T32, T23, T23)
Q723 = Κίνηση2(t - 9, T23, T33, T33)
uT23 = Vector(T23, T33)
ε05 = Line(T33, T15)
ε06 = Line(T16, T76)
T06 = Intersect(ε05, ε06)
uT33a = Vector(T33, T06)
uT33b = Vector(T06, T76)
Q733 = Κίνηση2(t - 10, T33, T24, T24)
Q724 = Κίνηση2(t - 11, T24, T15, T15)
Q715 = Κίνηση2(t - 12, T15, T06, T76)
ε07 = Line(T76, T67)
ε08 = Line(T51, T57)
T50 = Intersect(ε07, ε08)
uT76 = Vector(T76, T50)
uT50 = Vector(T50, T51)
uT51 = Vector(T51, T42)
Q776 = Κίνηση2(t - 14, T76, T67, T67)
Q767 = Κίνηση2(t - 15, T67, T50, T51)
Q751 = Κίνηση2(t - 17, T51, T42, T42)
uT42 = Vector(T42, T52)
Q742 = Κίνηση2(t - 18, T42, T52, T52)
ε09 = Line(T61, T16)
ε10 = Line(T77, T17)
T07 = Intersect(ε09, ε10)
uT52 = Vector(T52, T07)
uT07 = Vector(T07, T77)
Q752 = Κίνηση2(t - 19, T52, T43, T43)
Q743 = Κίνηση2(t - 20, T43, T34, T34)
Q734 = Κίνηση2(t - 21, T34, T25, T25)
Q725 = Κίνηση2(t - 22, T25, T16, T16)
Q716 = Κίνηση2(t - 23, T16, T07, T77)
ε12 = Line(T67, T61)
ε11 = Line(T77, ε01)
T60 = Intersect(ε12, ε11)
uT77 = Vector(T77, T60)
uT60 = Vector(T60, T61)
Q777 = Κίνηση2(t - 25, T77, T60, T61)
uT61 = Vector(T61, T71)
uT71 = Vector(T71, T17)
Q761 = Κίνηση2(t - 27, T61, T71, T71)
Q771 = Κίνηση2(t - 28, T71, T62, T62)
Q762 = Κίνηση2(t - 29, T62, T53, T53)
Q753 = Κίνηση2(t - 30, T53, T44, T44)
Q744 = Κίνηση2(t - 31, T44, T35, T35)
Q735 = Κίνηση2(t - 32, T35, T26, T26)
Q726 = Κίνηση2(t - 33, T26, T17, T17)
ε13 = Line(T27, ε01)
ε14 = Line(T17, T11)
T10 = Intersect(ε13, ε14)
ε16 = Line(T37, T73)
ε15 = Line(T21, T27)
T20 = Intersect(ε16, ε15)
ε18 = Line(T31, T37)
ε17 = Line(T47, T74)
T30 = Intersect(ε18, ε17)
uT17 = Vector(T17, T27)
uT27 = Vector(T27, T10)
uT10 = Vector(T10, T11)
Q717 = Κίνηση2(t - 34, T17, T27, T27)
Q727 = Κίνηση2(t - 35, T27, T10, T11)
ε19 = Line(T11, ε01)
ε20 = Line(T12, T72)
T02 = Intersect(ε19, ε20)
ε21 = Line(T21, T12)
ε22 = Line(T31, T13)
ε23 = Line(T13, T73)
ε24 = Line(T74, T54)
T03 = Intersect(ε21, ε23)
T04 = Intersect(ε22, ε24)
uT11 = Vector(T11, T02)
uT02 = Vector(T02, T72)
uT72 = Vector(T72, T36)
uT36 = Vector(T36, T46)
uT46 = Vector(T46, T20)
uT20 = Vector(T20, T21)
uT21 = Vector(T21, T03)
uT03 = Vector(T03, T73)
uT73 = Vector(T73, T55)
uT55 = Vector(T55, T65)
uT65 = Vector(T65, T30)
uT30 = Vector(T30, T31)
uT31 = Vector(T31, T04)
uT04 = Vector(T04, T74)
Q711 = Κίνηση2(t - 37, T11, T02, T72)
Q772 = Κίνηση2(t - 39, T72, T63, T63)
Q763 = Κίνηση2(t - 40, T63, T54, T54)
Q754 = Κίνηση2(t - 41, T54, T45, T45)
Q745 = Κίνηση2(t - 42, T45, T36, T36)
Q736 = Κίνηση2(t - 43, T36, T46, T46)
Q746 = Κίνηση2(t - 44, T46, T37, T37)
Q737 = Κίνηση2(t - 45, T37, T20, T21)
Q721 = Κίνηση2(t - 47, T21, T12, T12)
Q712 = Κίνηση2(t - 48, T12, T03, T73)
Q773 = Κίνηση2(t - 50, T73, T64, T64)
Q764 = Κίνηση2(t - 51, T64, T55, T55)
Q755 = Κίνηση2(t - 52, T55, T65, T65)
Q765 = Κίνηση2(t - 53, T65, T56, T56)
Q756 = Κίνηση2(t - 54, T56, T47, T47)
Q747 = Κίνηση2(t - 55, T47, T30, T31)
Q731 = Κίνηση2(t - 57, T31, T22, T22)
Q722 = Κίνηση2(t - 58, T22, T13, T13)
Q713 = Κίνηση2(t - 59, T13, T04, T74)
ZOOM = RotateText("- Zoom +", 90*°)
v3 = false
δ01 = Line(T14, T54)
δ02 = Line(T13, T53)
δ03 = Line(T12, T52)
δ04 = Line(T31, T35)
δ05 = Line(T21, T25)
δ06 = Line(T11, T15)
δ08 = Line(T53, T35)
δ09 = Line(T54, T45)
δ10 = Line(T55, δ09)
A51 = Intersect(ε19, δ03)
A52 = Intersect(δ02, ε21)
A53 = Intersect(δ01, ε22)
A54 = Intersect(ε03, ε25)
B52 = Intersect(δ08, δ05)
B53 = Intersect(δ09, δ04)
B54 = Intersect(δ10, ε04)
n2 = 14
vT01 = Vector(T13, A53)
vT02 = Vector(A53, T54)
vT03 = Vector(T54, B53)
vT04 = Vector(B53, T31)
Q714 = Κίνηση2(t - 1, T14, T05, T75)
Q502 = Κίνηση2(t - 1, T13, A53, T54)
Q503 = Κίνηση2(t - 3, T54, T45, T45)
Q504 = Κίνηση2(t - 4, T45, B53, T31)
vT05 = Vector(T31, T22)
vT06 = Vector(T22, T32)
vT09 = Vector(A54, T55)
vT10b = Vector(B54, T41)
vT12 = Vector(T51, T15)
Q505 = Κίνηση2(t - 6, T31, T22, T22)
vT07 = Vector(T32, A54)
vT10 = Vector(T55, B54)
vT11 = Vector(T41, T51)
Q506 = Κίνηση2(t - 7, T22, T32, T32)
Q507 = Κίνηση2(t - 8, T32, T23, T23)
Q508 = Κίνηση2(t - 9, T23, T14, T14)
Q509 = Κίνηση2(t - 10, T14, A54, T55)
Q510 = Κίνηση2(t - 12, T55, B54, T41)
Q511 = Κίνηση2(t - 14, T41, T51, T51)
Q512 = Κίνηση2(t - 15, T51, T42, T42)
Q513 = Κίνηση2(t - 16, T42, T33, T33)
Q514 = Κίνηση2(t - 17, T33, T24, T24)
Q515 = Κίνηση2(t - 18, T24, T15, T15)
vT16 = Vector(T15, T25)
Q516 = Κίνηση2(t - 19, T15, T25, T25)
δ11 = Line(T52, T25)
B51 = Intersect(δ06, δ11)
vT17 = Vector(T25, B51)
vT17b = Vector(B51, T11)
vT18 = Vector(T11, A51)
vT18b = Vector(A51, T52)
Q517 = Κίνηση2(t - 20, T25, B51, T11)
Q518 = Κίνηση2(t - 22, T11, A51, T52)
vT19 = Vector(T52, T34)
vT21 = Vector(T34, T44)
vT22 = Vector(T44, B52)
vT23 = Vector(B52, T21)
vT24 = Vector(T21, A52)
vT25 = Vector(A52, T53)
Q519 = Κίνηση2(t - 24, T52, T43, T43)
Q520 = Κίνηση2(t - 25, T43, T34, T34)
Q521 = Κίνηση2(t - 26, T34, T44, T44)
Q522 = Κίνηση2(t - 27, T44, T35, T35)
Q523 = Κίνηση2(t - 28, T35, B52, T21)
Q524 = Κίνηση2(t - 30, T21, T12, T12)
Q525 = Κίνηση2(t - 31, T12, A52, T53)
η1 = Line(T12, T32)
η2 = Line(T13, T33)
η3 = Line(T32, T23)
η4 = Line(T33, η3)
η5 = Line(T11, T13)
η6 = Line(T21, T23)
B31 = Intersect(η3, η5)
B32 = Intersect(η4, η6)
A31 = Intersect(ε19, η1)
A32 = Intersect(ε21, η2)
wT2 = Vector(T12, A32)
wT2b = Vector(A32, T33)
wT3 = Vector(T33, B32)
wT3b = Vector(B32, T21)
wT4 = Vector(T21, T31)
wT5 = Vector(T31, T13)
Q302 = Κίνηση2(t - 1, T12, A32, T33)
Q303 = Κίνηση2(t - 3, T33, B32, T21)
Q304 = Κίνηση2(t - 5, T21, T31, T31)
Q305 = Κίνηση2(t - 6, T31, T22, T22)
Q306 = Κίνηση2(t - 7, T22, T13, T13)
wT7 = Vector(T13, T23)
wT8 = Vector(T23, B31)
wT8b = Vector(B31, T11)
wT9 = Vector(T11, A31)
wT9b = Vector(A31, T32)
Q307 = Κίνηση2(t - 8, T13, T23, T23)
Q308 = Κίνηση2(t - 9, T23, B31, T11)
Q309 = Κίνηση2(t - 11, T11, A31, T32)
b1 = false
κείμενο2: "\frac{n·b·(n^2-1)}{2}+n·m=\frac{" + (LaTeX[n]) + "·" + (LaTeX[b]) + " ·(" + (LaTeX[n]) + " ^2-1)}{2}+" + (LaTeX[n]) + "·" + (LaTeX[m]) + "=\ovalbox{\Large \bold{\fgcolor{ff0000}{ " + (LaTeX[(n * m) + (((0.5 * n) * (n^(2) - 1)) * b)]) + "}}}"
TITLOS: "Τοποθετήστε τους  " + (n^(2)) + "  παρακάτω αριθμούς στο " + n + "x" + n + " τετράγωνο, ώστε αυτό να γίνει «ΜΑΓΙΚΟ»"
PROTOS = RotateText("Πρώτος (m)", 90*°)
BHMA = RotateText("Βήμα (b)", 90*°)
b2 = false
HELP1: "☛  Για να κατασκευάσουμε το “Μαγικό” τετράγωνο, κάνουμε τα εξής: 
Τοποθετούμε πρώτα το αριθμό " + m + " στο κεντρικό τετράγωνο της πρώτης γραμμής. 
Στη συνέχεια τον επόμενο αριθμό τον τοποθετούμε κάθε φορά στο επάνω δεξιά
τετράγωνο. Αν αυτό είναι έξω απ΄το μαγικό τετράγωνο τότε τον τοποθετούμε στο 
τελευταίο τετράγωνο της στήλης ή της γραμμής στην οποία βρίσκεται. 
Αν είναι κατειλημμένο από άλλο αριθμό τότε τον τοποθετούμε στο ακριβώς από 
κάτω του. Το ίδιο κάνουμε αν το επάνω δεξιά τετράγωνο δεν βρίσκεται σε προέκ-
ταση ούτε γραμμής ούτε στήλης. 
Με τον τρόπο αυτό μπορούμε να κατασκευάσουμε μαγικά τετράγωνα με περιττό 
αριθμό γραμμών και στηλών."
a = false
AK01 = FromBase(K01, 10)
e2 = false
H02 = (-3, 5.54)
H01 = (-3.74, 5.56)
H03 = (-2.24, 5.54)
H04 = (-1.44, 5.54)
H05 = (-0.64, 5.54)
H06 = (0.15, 5.54)
H07 = (0.91, 5.54)
H08 = (1.75, 5.54)
H09 = (2.53, 5.54)
H10 = (3.33, 5.54)
H11 = (4.09, 5.54)
H12 = (4.93, 5.54)
H13 = (5.73, 5.54)
H14 = (6.49, 5.54)
H15 = (7.27, 5.54)
H16 = (8.09, 5.54)
H17 = (8.89, 5.54)
H18 = (9.67, 5.54)
H19 = (10.47, 5.54)
H20 = (11.27, 5.54)
H21 = (12.05, 5.54)
H22 = (12.85, 5.54)
H23 = (13.63, 5.54)
H24 = (14.43, 5.54)
H25 = (15.23, 5.54)
H26 = (-3.76, 5.13)
H27 = (-3.04, 5.11)
H28 = (-2.25, 5.11)
H29 = (-1.44, 5.11)
H30 = (-0.64, 5.11)
H31 = (0.15, 5.11)
H32 = (0.95, 5.11)
H33 = (1.73, 5.11)
H34 = (2.53, 5.11)
H35 = (3.33, 5.11)
H36 = (4.11, 5.11)
H37 = (4.93, 5.11)
H38 = (5.71, 5.11)
H39 = (6.49, 5.11)
H40 = (7.31, 5.11)
H41 = (8.09, 5.11)
H42 = (8.87, 5.11)
H43 = (9.69, 5.11)
H44 = (10.45, 5.11)
H45 = (11.25, 5.11)
H46 = (12.03, 5.11)
H47 = (12.85, 5.11)
H48 = (13.65, 5.11)
H49 = (14.45, 5.11)
ArK01: "" + (LaTeX[m]) + ""
ArK02: "" + (LaTeX[m + b]) + ""
ArK03: "" + (LaTeX[m + (2 * b)]) + ""
ArK04: "" + (LaTeX[m + (3 * b)]) + ""
ArK05: "" + (LaTeX[m + (4 * b)]) + ""
ArK06: "" + (LaTeX[m + (5 * b)]) + ""
ArK07: "" + (LaTeX[m + (6 * b)]) + ""
ArK08: "" + (LaTeX[m + (7 * b)]) + ""
ArK09: "" + (LaTeX[m + (8 * b)]) + ""
ArK10: "" + (LaTeX[m + (9 * b)]) + ""
ArK11: "" + (LaTeX[m + (10 * b)]) + ""
ArK12: "" + (LaTeX[m + (11 * b)]) + ""
ArK13: "" + (LaTeX[m + (12 * b)]) + ""
ArK14: "" + (LaTeX[m + (13 * b)]) + ""
ArK15: "" + (LaTeX[m + (14 * b)]) + ""
ArK16: "" + (LaTeX[m + (15 * b)]) + ""
ArK17: "" + (LaTeX[m + (16 * b)]) + ""
ArK18: "" + (LaTeX[m + (17 * b)]) + ""
ArK19: "" + (LaTeX[m + (18 * b)]) + ""
ArK20: "" + (LaTeX[m + (19 * b)]) + ""
ArK21: "" + (LaTeX[m + (20 * b)]) + ""
ArK22: "" + (LaTeX[m + (21 * b)]) + ""
ArK23: "" + (LaTeX[m + (22 * b)]) + ""
ArK24: "" + (LaTeX[m + (23 * b)]) + ""
ArK25: "" + (LaTeX[m + (24 * b)]) + ""
ArK26: "" + (LaTeX[m + (25 * b)]) + ""
ArK27: "" + (LaTeX[m + (26 * b)]) + ""
ArK28: "" + (LaTeX[m + (27 * b)]) + ""
ArK29: "" + (LaTeX[m + (28 * b)]) + ""
ArK30: "" + (LaTeX[m + (29 * b)]) + ""
ArK31: "" + (LaTeX[m + (30 * b)]) + ""
ArK32: "" + (LaTeX[m + (31 * b)]) + ""
ArK33: "" + (LaTeX[m + (32 * b)]) + ""
ArK34: "" + (LaTeX[m + (33 * b)]) + ""
ArK35: "" + (LaTeX[m + (34 * b)]) + ""
ArK36: "" + (LaTeX[m + (35 * b)]) + ""
ArK37: "" + (LaTeX[m + (36 * b)]) + ""
ArK38: "" + (LaTeX[m + (37 * b)]) + ""
ArK39: "" + (LaTeX[m + (38 * b)]) + ""
ArK40: "" + (LaTeX[m + (39 * b)]) + ""
ArK41: "" + (LaTeX[m + (40 * b)]) + ""
ArK42: "" + (LaTeX[m + (41 * b)]) + ""
ArK43: "" + (LaTeX[m + (42 * b)]) + ""
ArK44: "" + (LaTeX[m + (43 * b)]) + ""
ArK45: "" + (LaTeX[m + (44 * b)]) + ""
ArK46: "" + (LaTeX[m + (45 * b)]) + ""
ArK47: "" + (LaTeX[m + (46 * b)]) + ""
ArK48: "" + (LaTeX[m + (47 * b)]) + ""
ArK49: "" + (LaTeX[m + (48 * b)]) + ""

Tool: Κίνηση1
Input: a, E, F
Output: A

A: E + (a * (F - E))

Tool: Κίνηση2
Δρομέας (από 0 έως 2) , Σημείο Α , Σημείο Β , Σημείο Γ
Input: a, A, B, C
Output: D

z: (1 + sgn(4 - a + 0.001)) / 2
u: (1 + sgn(1 - a + 0.001)) / 2
v: (1 + sgn(2 - a + 0.001)) / 2
w: (1 + sgn(3 - a + 0.001)) / 2
a3: ((((1 - u) * (1 - v)) * w) * z)
a1: (((u * v) * w) * z)
a5: ((((1 - u) * (1 - v)) * (1 - w)) * (1 - z))
a2: ((((1 - u) * v) * w) * z)
a4: ((((1 - u) * (1 - v)) * (1 - w)) * z)
c: (a2 * (a - 1)) + a3 + a4 + a5
b: (a1 * a) + a2 + a3 + a4 + a5
D: A + (b * (B - A)) + (c * (C - B))

Tool: Κίνηση3
Δρομέας(από 0 έως 3) ,Σημείο Α,Σημείο Β, Σημείο Γ , Σημείο Δ
Input: a, A, B, C, H
Output: D

u: (1 + sgn(1 - a + 0.001)) / 2
v: (1 + sgn(2 - a + 0.001)) / 2
w: (1 + sgn(3 - a + 0.001)) / 2
a3: (((1 - u) * (1 - v)) * w)
a1: ((u * v) * w)
a5: (((1 - u) * (1 - v)) * (1 - w))
a2: (((1 - u) * v) * w)
a4: (((1 - u) * (1 - v)) * (1 - w))
c: (a2 * (a - 1)) + a3 + a4
d: (a3 * (a - 2)) + a4
b: (a1 * a) + a2 + a3 + a4 + a5
D: A + (b * (B - A)) + (c * (C - B)) + (d * (H - C))

Tool: Διαίρεση Τμήματος Σε Ισα μέρη (command ΔιαίρεσηΤμήματοςΣεΙσαμέρη)
Σημείο , Σημείο, Αριθμός
Input: A, B, n
Output: λίστα1

λίστα1 = Sequence(A + (j * (B - A) / n), j, 1, n, 1)