Growing up, it was easy to agree with the teacher that 1+1 = 2. Saying anything contrary to this knowledge would be interpreted as mere ignorance and a lack of basic understanding. However, nature has taught me that things do not have to be the way we know them to be all the time. A twist and turn of the norm can provide answers to long unanswered questions in the history of mathematics. Research into number theory enabled me to understand the unexpected and interesting relationship that exists between various numbers. For instance, is it possible to have the sum of two squares as a square? Is it logical to say that 42 + 32 = 52 and 52 +122 = 132? Research has shown that these are Pythagorean triples that lack sense and understanding of the normal layman without additional knowledge on mathematics.
The Pythagorean Theorem
The Pythagorean Theorem is familiar with most high school students, whereby a² + b² = c². According to this formula, the sum of squares on the side of a right-angled triangle adds up to the square of the hypotenuse. The most famous triangle of this kind is the 3, 4, 5 sides. Other examples are 32+42=52, 82+152=172. This triple has changed how statisticians and mathematicians approach mathematical problems. Its use has been of essence since days immemorial in that they were used in Babylonian tablets that contain list of large and small triples that indicated that the Babylonians had a specialized method of producing them, such as the use of trigonometric tables. In Ancient Egypt, mathematicians often produced a right angle through the application of a rough and ready method (Veljan 259). One person would mark 12 equal segments on a rope and tie into a tight loop, after which they would hold it taught to form a 3-4-5 triangle.
Appreciate the Intricacy and Beauty of Mathematics
Such practical mechanisms are innate and are the main forces that drive innovation and creativity in the world. However, these innovations cannot be achieved without the efficient application of mathematics and related formulas. Although practical methods like those adopted by the Babylonians and Egyptians have ceased to exist due to advancements in technology, the effectiveness of the Pythagorean triples in life cannot be disputed. An expert in these theorems is likely to ask one to research on the music of Beethoven and the art of Rembrandt in that these aspects exemplify the beauty of interaction and connection. Numbers interact with each other in a similar sense as the beauty of composition, symphony or painting. However, one must begin to understand and appreciate the intricacy and beauty of mathematics to appreciate this connection. Understanding this connection should be the basis upon which mathematical formulas should be derived. This would help one to verify the existence or non-existence of the notion that 1+1=3.
The Pythagorean Theorem in Architecture
From the basic understanding of a Pythagorean Theorem, it is possible to understand the source of a Pythagorean triple. This is to say that, if a² + b²= c² then (a² + b² = c²) will give (da)² + (db)² = d²(a² + b² ) = d²c² = (dc)² . With technological advancement, it is easy to understand how one can derive the Pythagorean triples, such as (3, 4, 5), (5, 12, 13), (8, 15, 17), (20, 21, 29), (9, 40, 41), (11, 60, 61), (33, 56, 65), among others. Looking at the list of provided numbers, it is clear that a and c are odd numbers while b is an even number. With this understanding, it easy identifies the reason why life can deem difficult without the application of this theorem. For instance, woodworking, construction projects, and architecture would be challenging to understand without the application of the Pythagorean Theorem. An individual would understand the slope of the roof if they know the height and length that the roof is expected to cover.
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The Pythagorean Theorem in Navigation
Apart from construction and architecture, it would have been almost impossible to navigate without the application of the Pythagorean Theorem (Kadison 4178). Early explorers achieved their navigation objectives through the application of this phenomenon, which enabled them to identify the shortest distance to their destination. Those navigating to a destination that is 300 miles to the South and 400 miles to the West found the distance that the ship would be needed to travel to the destination. The distance was presumed to appear like the legs of a triangle, which were connected with a diagonal. This premise is also applied by planes when descending by calculating distance from the airport and height from the ground. This is the reason why I believe that the beauty of life is in the numbers; the intricacy and connection of mathematics.
Citation：
Veljan, Darko. “The 2500-year-old Pythagorean theorem.” Mathematics Magazine 73.4 (2000): 259-272.
Kadison, Richard V. “The Pythagorean theorem: I. The finite case.” Proceedings of the National Academy of Sciences 99.7 (2002): 4178-4184.
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