Hypotenuse Essays

​Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are two legs of a right triangle and c is the hypotenuse, the longest side of the triangle. This 1-inch long, simple, yet eloquent equation contains a beauty, a magic that is unnoticeable at first glance; I have been introduced to this beauty by Dartmouth alumni Professor Strogatz at an Engineering Diversity Weekend program last September. As I finished my breakfast, I had the opportunity to join the campus tour or attend a mock math class, named

Introduction A Pythagorean triple is an ordered triplet of positive integers (a,b,c) such that: a^2+b^2=c^2. It is evident that such integers correspond to the sides of a right triangle, a, b being the catheti (legs) and c being the hypotenuse of the triangle. The most well known Pythagorean triple is 3,4,5. As early as in the 8th grade I started feeling that knowing at least a few commonly used Pythagorean triples allows solving various geometry problems with a bigger ease. For example, it

The sum a triangle 's angles should add up to 180°.The formula that is used for a triangle is b+h+x=180.A right triangle sometimes has a missing angle such as 35+35+? The missing angle would be 90. The reason the sum a triangle 's angles should add up to 180°.The formula that is used for a triangle is b+h+x=180.A right triangle sometimes has a missing angle such as 35+35+? The missing angle would be 90.The reason the missing side would be 90 is because a right triangle has a right angle in it and

Some roulette players use a sequenced betting system. The set of numbers in the sequence determines the size of the bet in a system known as the Fibonacci roulette betting system. As you might have noticed, the name is taken from one of the greatest mathematicians of the Middle Ages. That's because this betting system is actually based on his homonymous number sequence—the Fibonacci numbers. A Bit of History Leonardo Fibonacci, also known as Leonardo of Pisa, presented to the world a sequence

Biography of Pythagoras Pythagoras’ experiences, education, and travels influenced his thinking that lead to the development of his theorem. Pythagoras is a famous mathematician and philosopher best known for his work on the theorem that is named after him called the Pythagorean theorem. According to the theorem, “for any right angle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side (Harkins 35). Pythagoras may not have invented this

(SAS), Angle-Side-Angle (ASA), Angle-Side-Angle (AAS), Angle-Angle (AA) and Hypotenuse-Leg (HL). The others

link in notes *insert pictures + make report format* In my mathematical investigation, I have chosen the topic geometry, focusing on 2 generalisations and conjectures. The aim of this investigation is to further understand the topic I have chosen and to be able to apply it in my daily life. I decided on the topic geometry as I feel that I am more interested in this topic as the school has not fully covered this topic. *historical background of polyhedrons and triangles* Euler’s Formula for polyhedron

Soccer which is also commonly known as football is a game that has been played since 1863. It´s a match between 11 players on each side and trying to get a ball that approximately weighs 1pound into a net. Soccer grounds can have different distances from one goal to the other or the whole ground in general. Distance can have different definitions but in this exploration, distance is the space between two things. In this case it will be the displacement from the position of the player and the ball

As I said in my cover letter, the Pythagorean theorem equation is a^2+b^2=c^2 and c^2 will always represent the hypotenuse which is the longest side of the right triangle while a^2 and b^2 can any of the other two sides. Look at Visual 6 to see an example of how to use Pythagorean theorem to solve for the side length of a triangle. Visual 6 Start with: a2 + b2

point on the bottom left corner and the other on the upper right corner of the meter stick- and then calculating the number of pixels that make up the X-axis and Y-axis distances between both points. Through the use of the Pythagorean Theorem, the hypotenuse was calculated. This value would essentially be the “true” number of pixels the meter stick represents. These steps were done once more for the vertically positioned meter stick. A discrepancy between both vertical and horizontal values for the

I need to find the area of rectangle ABCD. I know that ABCD is a rectangle with diagonals intersecting at point E. Segment DE equals 4x-5, segment BC equals 2x+6, and segment AC equals 6x. I predict that To find the area of rectangle ABCD I need to find out the base and height of the rectangle. The first step is to find what x equals. Since I know the intersecting line segments AC and DB are congruent that means when I times the equation 4x-5 for segment DE by two it will equal the equation

2.1.4 Estimate quantities to a tolerance acceptable in the context of the estimation Example 1: Estimating and measuring length Question John needs to measure the width of a window, to find out how much material he needs to buy to make a curtain. The curtain material costs R 55 per metre. John estimates the width of the window (using his arm) to be 1,9 metres wide. If Carl goes to the shop with this estimate: 1. How many metres of material would he need to buy? 2. How much would the material cost

Pythagoras Pythagoras is a famously known controversial ancient greek philosopher. Pythagoras is known as the first pure mathematician. Though much information about pythagoras mathematical achievements is not known, because unlike other greek mathematicians, pythagoras had no book or writings. The information known about pythagoras today, was recorded a few centuries after his death. Pythagoras is the son of Mnesarchus, he was born on a greek island in 570 BC. Pythagoras was known to be married

him go and apologised. They filled the hole and stop the draining; Johnnit was the town hero and got to stay on the long side of Mt. Potenuse near the town Wrightriangle. So next time you want to know what the long side of a right triangle aka the hypotenuse is, remember Johnnit and how he saved the town Wrightriangle and lived

8) Explain and evaluate the views of Anaximander regarding the nature of substance. Anaximander (610-546 BCE) was a famous philosopher known for his different, but correct point of view about the primary substance of the reality. He rejected to Thales, who said that “All is water”, and Anaximenes, who claimed that all objects are composed for air when he stated that the primary substance is in fact unlimited, or infinite. Even though Anaximander questioned about the existence of primary substance

The Start of Infinity This article briefly discusses the journey of the attempts to understand the concept of infinity. Ancient civilizations did not display having knowledge of conceptualizing infinity, but of course from the time people began to think about the world they lived in, questions about infinity arose. Ancient cultures did not define infinity as does modern mathematics but instead approached infinity as a philosophical concept. During the development of mathematics and science, the

of warning his audience about his proof of God’s existence is that just because we imagine God that does not mean God’s presence relies upon our thinking about this. Descartes’s sets a clear example, he brings math in perspective by saying that hypotenuse is the sum of 2 other sides of the triangle and that can be proven through the theory of Pythagorean theorem. Now that it is discovered, one does not need to go back get look for proof of this theory. One must accept it and move on. Similarly, Nature

boundaries in the family subsystem. Family boundaries may be clear, normal, weak, diffuse or rigid. The therapist must try to restructure the system, by observation and manipulation of interactions within a session. Behavioural sequences form a basis for hypotenuse of the families structure. Enactments and interactions are suggested to the family by the therapist as a way of understanding and diagnosing the structure, this provides a room for re-structuring and intervention within the family’s system. Structural

mathematicians were Euclid, Pythagoras and Archimedes. Euclid created a geometry textbook with 465 propositions and proofs about geometry titled Elements. Pythagoras invented the Pythagorean Theorem, which states that “the square of a right triangle’s hypotenuse equals the squared lengths of the two remaining sides.”(Ancient World History -------) Lastly, Archimedes, a scientist, estimated the accurate value of Pi. Most of these theories although they were not always accurate they led to further

Many of the most famous ancient philosophers and philosophical ideals originated from Greece. In his paper, The Ancient Greeks, Part One: The Pre-Socratics, Dr. C. George Boeree explains different aspects of ancient Greek philosophy. Firstly, he explains several of the reasons as to why philosophy became so prominent in Greece compared to other nations during the same time period. Next, Dr. Boeree defines some of the basic subcategories and subsections of philosophy, mainly metaphysics, epistemology