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# Magic Wheels

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### Magic Wheels

1. 1. MAGIC WHEELSAugust 1, 2012 Tofique Fatehi tofiquef@yahoo.com http://tofique.fatehi.us WHEEL 1Circumference = 1 unitTake a wheel that is one unit in circumference. Mark a point A on the circumference. If the wheel isrolled on a flat surface for one full turn, from A to A, it will have moved one unit. WHEEL 2Circumference = 3 unitsTake a wheel that is three units in circumference. Mark a point A on the circumference and anotherpoint B which is circumferentially one unit away from A. If the wheel is rolled on a flat surface fromA to B along the shorter arc, it will have moved one unit, whereas if it is moved from B to A alongthe longer arc, it will have moved two units. And if it moved a full turn, A to A, then it will havemoved three units. WHEEL 3Circumference = 7 unitsThis wheel is 7 units in circumference, and has 3 points (A, B and C) marked on the circumference,dividing the circumference into 3 unequal arcs of 1 unit (AB), 2 units (BC) and 4 units (CA). A to B AB 1 unit B to C BC 2 units A to B to C ABC 3 units C to A CA 4 units C to A to B CAB 5 units B to C to A BC 6 units A to A ABCA 7 unitsMagic Wheels© 2012 Tofique Fatehi Page 1
2. 2. WHEEL 4Circumference = 13 unitsWheel 4 is a bigger wheel that is divided into 4 arcs by 4 points (A, B, C, D). The arc lengths are 1, 2,6, and 4 units. You could move any number of units, from 1 through 13, like this: AB 1 unit BC 2 units ABC 3 units DA 4 units DAB 5 units CD 6 units DABC 7 units BCD 8 units ABCD 9 units CDA 10 units CDAB 11 units BCDA 12 units ABCDA 13 unitsWheel 4 has another alternative to arc lengths - instead of 1, 2, 6, and 4 units it is also possible tohave 1, 3, 2, and 7 units. WHEEL 5Circumference = 21 unitsWheel 5 has 5 Arcs of 1, 3, 10, 2, 5 units. You can use it to measure any integer units from 1 to 21. WHEEL 6Circumference = 31 unitsWheel 6 is a very big wheel with 6 arcs of 1, 2, 5, 4, 6, and 13 units. It can move any integer unitsfrom 1 to 31.Wheel 6 has 5 alternatives to divide the circumference.1, 2, 5, 4, 6, and 13 units, as above1, 2, 7, 4, 12, and 5 units1, 3, 2, 7, 8 and 10 units1, 3, 6, 2, 5 and 14 units1, 7, 3, 2, 4 and 14 unitsMagic Wheels© 2012 Tofique Fatehi Page 2