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Mathematics & Economics

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Math Problem

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# Discovering the Square Triangle Numbers: Evaluation (Math Problem Sample)

Instructions:

Please check the math or the exploration and make changes accordingly Make sure the criteria is followed throughout the exploration using the pdf attached Write and introduction, conclusion and evaluation

source..Content:

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DISCOVERING THE SQUARE - TRIANGULAR NUMBERS

Introduction

In the ancient world, the Greeks used to play with numbers one of their most favourite number games was that involving the use of polygons. Such number games were kind of interesting to an extent that mathematician decided to write a lot of literature about them. Organization of Polygonal numbers can be in such a way that they form polygonal matrices, made of positive integer elements. A triangle in this regard is a three-sided polygon while a square is a four-sided polygon.

Evaluation

Numbers like 1, 3, 6, 10, 15, 21, â€¦. are triangular numbers (Lafer). They form an array of a triangular pattern. Also, note that the difference between any two succeeding triangular numbers increases by a given factor, so that prediction of the next integer can be possible. The patterns formed by triangular numbers are as shown in the figure below:

Figure 1: Triangular numbers CITATION Phi16 \l 2057 (Lafer)

On the other hand the numbers 1, 4, 9, 16, 25,â€¦ are commonly known as the perfect squares. The perfect squares have square roots which are integers. The patterns associated with perfect squares form squares as shown in figure 2 shown below:

Figure 2: Square numbers CITATION Ref12 \l 2057 (Refik and KaraatlÄ±)

Other polygons like pentagons, hexagons, octagons, among others can also be given the same considerations to form number patterns. Triangular numbers form a sequence that can be expressed as 1, 3, 6, â€¦., n(n+1)/2, â€¦.. Some of these triangular numbers are also perfect squares. For example 1,...

Professor

Course

Date

DISCOVERING THE SQUARE - TRIANGULAR NUMBERS

Introduction

In the ancient world, the Greeks used to play with numbers one of their most favourite number games was that involving the use of polygons. Such number games were kind of interesting to an extent that mathematician decided to write a lot of literature about them. Organization of Polygonal numbers can be in such a way that they form polygonal matrices, made of positive integer elements. A triangle in this regard is a three-sided polygon while a square is a four-sided polygon.

Evaluation

Numbers like 1, 3, 6, 10, 15, 21, â€¦. are triangular numbers (Lafer). They form an array of a triangular pattern. Also, note that the difference between any two succeeding triangular numbers increases by a given factor, so that prediction of the next integer can be possible. The patterns formed by triangular numbers are as shown in the figure below:

Figure 1: Triangular numbers CITATION Phi16 \l 2057 (Lafer)

On the other hand the numbers 1, 4, 9, 16, 25,â€¦ are commonly known as the perfect squares. The perfect squares have square roots which are integers. The patterns associated with perfect squares form squares as shown in figure 2 shown below:

Figure 2: Square numbers CITATION Ref12 \l 2057 (Refik and KaraatlÄ±)

Other polygons like pentagons, hexagons, octagons, among others can also be given the same considerations to form number patterns. Triangular numbers form a sequence that can be expressed as 1, 3, 6, â€¦., n(n+1)/2, â€¦.. Some of these triangular numbers are also perfect squares. For example 1,...

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