On square sum graphs
... Cn1 : u1 , u2 , . . . , un , u1 and Cn2 : v1 , v2 , . . . , vn , v1 be the first two copies of Cn , where u1 v1 be the path P2 joining Cn1 and Cn2 . Define f : V (G) → {0, 1, 2, . . . , kn − 1} as follows. Start from vertex u1 of Cn1 , visit all the vertices of Cn1 using BFS algorithm and label the ...
... Cn1 : u1 , u2 , . . . , un , u1 and Cn2 : v1 , v2 , . . . , vn , v1 be the first two copies of Cn , where u1 v1 be the path P2 joining Cn1 and Cn2 . Define f : V (G) → {0, 1, 2, . . . , kn − 1} as follows. Start from vertex u1 of Cn1 , visit all the vertices of Cn1 using BFS algorithm and label the ...
Geometric and Harmonic Variations of the Fibonacci Sequence
... a set of initial conditions {G1 , G2 , ..., Gr }. Other modifications include a nondeterministic version that allows for randomness in the values of the terms of the sequence, while still having successive terms depend on the previous two: one such recurrence is given by tn+2 = αn+2 tn+1 + βn+2 tn w ...
... a set of initial conditions {G1 , G2 , ..., Gr }. Other modifications include a nondeterministic version that allows for randomness in the values of the terms of the sequence, while still having successive terms depend on the previous two: one such recurrence is given by tn+2 = αn+2 tn+1 + βn+2 tn w ...
Constructions of the real numbers
... we believe to know about the real numbers so that we can start from scratch. The set of real numbers R is widely introduced as the (unique) set satisfying the axioms for a complete ordered field. While different axiomatic descriptions of ordered fields are usually quite similar, there exist various ...
... we believe to know about the real numbers so that we can start from scratch. The set of real numbers R is widely introduced as the (unique) set satisfying the axioms for a complete ordered field. While different axiomatic descriptions of ordered fields are usually quite similar, there exist various ...
Section 5.4 Factoring Trinomials, a > 1
... 3 and 5 (or 1 and 15). We’re not looking for numbers that add to get 15, like 7 and 8. Yet, doesn’t it seem strange when we multiply (x + 2)(x + 3) and get x2 + 5x + 6? Where’s the multiplication in x2 + 5x + 6? Why is there so much addition in x2 + 5x + 6? Isn’t that supposed to be a product, a mul ...
... 3 and 5 (or 1 and 15). We’re not looking for numbers that add to get 15, like 7 and 8. Yet, doesn’t it seem strange when we multiply (x + 2)(x + 3) and get x2 + 5x + 6? Where’s the multiplication in x2 + 5x + 6? Why is there so much addition in x2 + 5x + 6? Isn’t that supposed to be a product, a mul ...
