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Math exploration of Pascals Triangle

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Moreover, tis was in relation to the question of taking into consideration the sun and the corresponding six planets, wich were known at that time in combinations of a single element each period, wich is repeated each time. Fbonacci in 122 independently wrote down the solutions of the binomial equation of the third degree although it was known in India and Middle East (Birken & Anne, p. Fbonacci was also the first European mathematician to make use of the Arabic numerals thus rendering he Roman numeral system obsolete.

wrote his work titled “Treatise on the Arithmetical Triangle” in 1654 but was published until 1665. Tis work had an immense role in the development of the probability theory, teory of convergent and divergent series, drivative and integral calculus. Te numbers in each row except the one at the apex of the triangle can be attained by adding two underlying adjacent numbers within the aforementioned row. I true even for the numbers bordering the triangle if there is assumption that there are invisible zeros that extend to the sides rowThere are several observations that can be from the Pascal’s triangle.

Te first observation is that all the numbers are positive. Oly positive numbers can be generated including additional 1’s or adding existing positive numbers. Tere exists a vertical line within the symmetry through the apex of the triangle. Te identical thing is undertaken on both sides of the line of symmetry, ad therefore the same results are obtained (Cullinane, p. Mreover, i is in agreement with the fundamental idea in mathematics where if you do the same to same subjects, te same results.

Rws that are parallel to the edges of the triangle also depict interesting patterns. Fr example 1, 3 6, 10, 15 and so on are just the sums of (1), 1+2), 1+2+3), 1+2+3+4) and so on. Mreover, i is swift elaboration of generations’ methods of the numbers, ad sometimes referred to as triangular numbers because they are generated by an equilateral triangle (Bassarear, p178-212). Te figure also shows that some rows contain exclusively odd numbers, ad each of the numbers is one than a power of 2 such as 1, 3 7, 15, ad 31.

Te explanation to this is that since the addition of prevailing even and corresponding odd number, wich give an even number and at the edges. ..

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