Bermuda Triangle

At about twenty centuries ago there was an amazing discovery about right angled triangles: “In a right angled triangle the square of the hypotenuse is equal to the sum of squares of the other two sides.” It is called Pythagoras Theorem and can be written in one short equation: a²+b²=c² where c is the longest side of triangle and a and b are the other two sides. Pythagoras was born in the island of Samos in 570 BC in Greek in the eastern Agean. He was the son of Mnesarchus and his mother's name…

We can easily convert this into Cartesian form by replacing z by x+iy |(x+iy)-(-3 +2i)|=5 |(x+3) + i(y-2)|=5 √(〖(x+3)〗^2+〖(y-2)〗^2 ) =5 or 〖(x+3)〗^2+〖(y-2)〗^2=25 Which is the exact form of a Cartesian equation of a circle with a center of (-3, 2) and a radius of 5 We could check if a particular point lies on the circle Ex. z2=1-3i Substituting into the equation of the circle, with z replaced by z2=1-3i |(1-3i) - (-3 + 2i)|=5 |4-5i|=5 √(4^2+〖(-5)〗^2 ) =5 41=5, which is not true, thus z2 does not…

While it is necessary to delegate different tasks to team members, leaders also possess the responsibility of their team as a whole. While my Robotics team was revising our robot for the VEX Robotics Mid-Atlantic Championships, I made sure to keep track of the team’s progress in the engineering notebook, as well as supervise the work of my fellow team members. At Governor’s School, I will make sure to collaborate and contribute ideas, as well as provide leadership skills such as guidance,…

The theorem used to find the hypotenuse, adjacent, or opposite sides of a triangle is also used in Euclidian Geometry. “A” squared plus “B” squared equals “C” squared is the formula used in the theorem. For example, we are given two numbers in the sides of a triangle; if we are given the adjacent and opposite sides, and we must figure out the hypotenuse, we will be required to use the Pythagorean Theorem. The two numbers…

Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It does not tell us exactly which right triangle to draw.…

non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic lemmas, one is on the fact “Among all the pedal’s…

The sculptural portrait of Faustina the Elder is made of marble and was sculpted between the years of 140 and 160 A.D. She is a Roman piece by an unknown artist, and is housed in the Getty Villa. Faustina is composed of strong lines and shapes to draw the viewer into the vertical dominant composition. Multiple forms break down into triangular shapes that bring the eye up and down the length of the piece, in order to add some movement to her otherwise static pose. Faustina the Elder stands…

because I realized that the lines O1O, O1O2, and O2O1, form a triangle, I realized that if that triangle was a right triangle I could find the distance between O1, and O. To prove that triangle OO1O2 is a right triangle I used the radii of O1, I realized that the sides of triangle PO1Q, O1P, and O1Q, are radii, and therefore they are equal. Since they are equal, the triangle PO1Q, is an isosceles triangle. In an isosceles triangle the base angles are congruent , so that means that angle Q is…

The Van Hiele Theory applies to the article “Freedom Quilts and the Underground Railroad.” The three level of Van Hiele are used in the Freedom Quilt Activity. These three levels are recognizing figures by their appearance, recognizing/analyzing figures by their properties or components, and forming abstract definitions and classifying figures by their elaborating on their interrelationships. Students will be scaffolding as they are analyzing the shapes. At the second part of the activity, the…

Pythagoras’s brown hair was mussed like he hadn’t slept well and there were shadows under his green eyes. I suspected that he had woken from his “dream from the gods” and had stayed up pondering his options. Why would he have come to my house and arranged triangles from firewood? “It’s nothing.” I said quickly. “And it’s not a book. I can’t read.” That was a lie, I could read very well. “Go home. Why are you at my house anyways?” “Don’t burn the book.” Pythagoras warned me, and I got the…