The smallest Magic Triangle is the 3 x 3 pattern with three different numbers arranged in circles along three sides so that their sum is the same along each side. We call the sides as legs and represent them as L1, L2 and L3. Small circles are drawn at the vertices as well as on each leg, to fill the numbers. The circles at the vertices are named V1, V2 and V3. By increasing the number of circles equally along the legs, different patterns of Magic Triangles such as (3 x 3), (3x 4), (3 x 5) etc. are obtained.
3 x 3 Magic Triangles
6 consecutive numbers of an Arithmetic Progression are used here.
V1 , V2 , V3 - Vertex 1, Vertex 2, Vertex 3 Usually the first number of number series is written in V1 .
L1 , L 2, L3 - Leg 1, Leg 2, Leg 3 of the triangle.
The following letters are used in formulas.
F - The first number of the progression
S - Sum of terms /numbers along each leg.
D - The common difference between adjacent numbers of the series.( In our combinations D is always treated as Natural Number)
L - The last number of the progression.