Circumradius and Inradius of a 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 triangles, the pedal triangle whose area is one fourth of area of the reference triangle has maximum area” and other is related to the “area of Ex-Touch triangle”. Notations: Let ABC be a triangle. We…
Background Knowledge About the Bermuda Triangle There are many mysterious phenomenons in our world that we simply cannot explain. The Bermuda Triangle is an area where the waves change quickly and unpredictably. It is located in the North Atlantic Ocean between Florida, Puerto Rico, and Bermuda. There have been many incidents of missing ships and planes considering it is a frequently traveled area, mostly used for shipping. Many have related these disappearances to paranormal activity and a…
planes and ships have randomly disappeared, and all in the same area - the Bermuda Triangle. One of the biggest disappearances includes Flight MH370. Many have speculated about the cause, or causes. Some of the causes are supernatural, including aliens, Atlantis death rays, and large, giant sea monsters, like krakens. Other theories are completely natural, like methane crystals, large waves, and human stupidity. Most have settled for the theory of methane crystals and rogue and tidal waves. But…
THE SINE FUNCTION (SIN) Sine function is an odd function. 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…
The Bermuda Triangle The Conspiracy By Damon Scott II Ever since the Columbus incident,when Columbus went to explore in 1492,his compass wasn’t working and now he started to panic because he didn’t know where he was, then his crew panicked and somehow ended up back where they were. Edward Van Winkle, claims that strange things are happening, but Larry Kusche thinks a lot different. Edward Van Winkle claims that pirates control the Bermuda Triangle waters or Atlantis’s energy floor from the…
as one of the strangest places on earth, the Bermuda Triangle holds many mysteries that go unexplained. Nicknamed the ‘Devil 's Triangle”, the Bermuda Triangle got its name from being located in the center of three islands that form the shape of a triangle. There have been over thousands of ship and plane disappearances, like the disappearance of those 5 bomber planes. Why have they never found wreckage or bodies? What happened to the ships or even the people? These are some questions no one…
Imagine being in a plane and it randomly goes down over the Bermuda Triangle. Also known as the Devil’s Triangle, Bermuda Triangle is a general area in the western part of the Atlantic Ocean where planes and ships have mysteriously disappeared over the years. It received it’s name from a magazine after an extremely popular disappearance known as Flight 19. Nobody knows for sure if the Bermuda Triangle is real because science cannot explain many disappearances including the USS Cyclops, Ellen…
The Bermuda Triangle Mystery Throughout time the Bermuda Triangle has been home to several different disappearances. Ships, planes, and people have all gone missing in this odd area. Mystery arose starting as early as the 1800s. Some believe in different theories as to why there have been so many disappearances such as hexagonal clouds acting as air bombs, a strange ocean floor, and erratic weather conditions but, nothing proves to be the answer to these peculiar occurrences. The mystery of…
Introduction I’m going to start this paper with introducing the history of Pascal’s Triangle, time ranging from 2nd century BC to 18th century AD. Among all the academic works by ancient mathematicians, I’m going to focus on Jiu Zhang Suan Shu [Nine Chapters on the Mathematical Art] composed by Chinese scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After…
For years, people have tried to understand: Why do such mysterious activities occur in the Bermuda Triangle? Ships have vanished without a trace and aircraft disappear with no sign of where they went. There have been countless cases where aircraft and boats have shown no signs or radioed that they were in distress. Boats have showed up without any crew members and there is no damage to the boat. There have been many possible reasons that have surfaced in recent years. From scientific reasons to…