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# Math exploration of Pascals Triangle Essay Example

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## Math exploration of Pascals Triangle

Moreover, this was in relation to the question of taking into consideration the sun and the corresponding six planets, which were known at that time in combinations of a single element each period, which is repeated each time.Fibonacci 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, pp. Fibonacci was also the first European mathematician to make use of the Arabic numerals thus rendering he Roman numeral system obsolete.Blaise Pascal wrote his work titled “Treatise on the Arithmetical Triangle” in 1654 but was published until 1665. This work had an immense role in the development of the probability theory, theory of convergent and divergent series, derivative and integral calculus.The 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. It true even for the numbers bordering the triangle if there is assumption that there are invisible zeros that extend to the sides of each rowThere are several observations that can be from the Pascal’s triangle. The first observation is that all the numbers are positive. Only positive numbers can be generated including additional 1’s or adding existing positive numbers.There exists a vertical line within the symmetry through the apex of the triangle. The identical thing is undertaken on both sides of the line of symmetry, and therefore the same results are obtained (Cullinane, pp. Moreover, it is in agreement with the fundamental idea in mathematics where if you do the same thing to the same subjects, the same results.Rows that are parallel to the edges of the triangle also depict interesting patterns. For 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. Moreover, it is swift elaboration of generations’ methods of the numbers, and sometimes referred to as triangular numbers because they are generated by an equilateral triangle (Bassarear, pp178-212).The figure also shows that some rows contain exclusively odd numbers, and each of the numbers is one less than a perfect power of 2 such as 1, 3, 7, 15, and 31. The explanation to this is that since the addition of prevailing even and corresponding odd number, which give an even number and at the edges

Works Cited

Birken, Marcia, & Anne C. Coon. Discovering Patterns in Mathematics and Poetry. Amsterdam: Rodopi, 2008.

Benson, Steven. Facilitators Guide to Ways to Think About Mathematics. Thousand Oaks, CA: Corwin Press, 2004.

Cullinane, Michael J. A Transition to Mathematics with Proofs. Burlington, MA: Jones & Bartlett Learning, 2013.

Bassarear, Tom. Mathematics for Elementary School Teachers. Belmont, CA: Brooks/Cole, 2011.

Fox, Sue, and Liz Surtees. Mathematics Across the Curriculum: Problem-solving, Reasoning, and Numeracy in Primary Schools. London: Continuum International Pub. Group, 2010.

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