# Columella's Formula

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Presents guidelines for teachers in discussing the March 22, 2004 issue of "Scholastic Math" magazine in class. Activities on circle graphs; Tips on enabling students to understand and remember the formula for the area of a circle; Exercises in determining if two ratios are equal.

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Let G be a tree. It is proved that for any vertex v of G âˆ£Vâˆ£ + âˆ‘qâˆŠV [d(q) - 2]l(v,q) = 1 in which d(q) is the degree of the vertex q, and l(v, q) is the distance between v and q in G. This result enable us to derive a formula concerning the average distance for some...

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A Smarandachely k-constrained labeling of a graph G(V,E) is a bijective mapping f : V ? E ? {1, 2, .., |V| + |E|} with the additional conditions that |f(u) - f(v)| ? k whenever uv ? E, |f(u)-f(uv)| ? k and |f(uv)-f(vw)| ? k whenever u ? w, for an integer k ? 2. A graph G which admits a such...

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Let G be a graph and f : V (G) ? {1, 2, 3, ï¿½, p + q} be an injection. For each edge e = uv and an integer m ? 2, the induced Smarandachely edge m-labeling f*S is defined by f*S(e) = ?f(u) + f(v)/m? Then f is called a Smarandachely super m-mean labeling if f(V (G)) ? {f*(e) : e ? E(G)} = {1,...

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Let G1 = (V1,E1), G2 = (V2,E2) be two graphs. For a chosen edge set E ? E2, the Smarandache VE-product G1 ï¿½VE G2 of G1, G2 is defined by V (G1 ï¿½VE G2) = V1 ï¿½ V2, E(G1 ï¿½VE G2) = {(a, b)(a', b')|a = a', (b, b') ? E2, or b = b', (a, a') ? E1} ? {(a, b)(a', b')|(a, a') ? E1 and...

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Given an arbitrary non-empty subset M of vertices in a graph G = (V,E), each vertex u in G is associated with the set fï¿½M(u) = {d(u, v) : v ? M, u ? v}, called its open M-distance-pattern. A graph G is called a Smarandachely uniform k-graph if there exist subsets M1,M2, ï¿½ï¿½ï¿½...

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Questions concerning the accuracy of numerical methods for differential equations are often analysed using B-series and other formulations based on rooted trees. The analysis of numerical methods, such as Rosenbrock and certain exponential methods, requires an additional algebraic structure to...

- On k-th Power of Upper Bound Graphs. Tsuchiya, Morimasa // Annals of Combinatorics;2003, Vol. 7 Issue 4, p495
Presents a study that considered finite undirected simple graphs. Characterization of upper bound graphs; Properties on squares of upper bound graphs; Information on the properties of simple vertex; Mathematical theorems used in the study; Details on mathematical formulas and equations.