The Sierpinski Triangle
Deep within the realm of fractal math lies a fascinating triangle filled with unique properties and intriguing patterns. This is the Sierpinski Triangle, a fractal of triangles with an area of zero and an infinitely long perimeter. There are many ways to create this triangle and many areas of study in which it appears.
Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in the early twentieth century. Although it appears simple, the Sierpinski Triangle is actually a complex and intriguing fractal. Fractals have been studied since 1905, when the Mandelbrot Set was discovered, and since then have been used in many
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Using this formula:
Log(4)
= Log(2)
Log(22)
= Log(2)
2Log(2)
= Log(2)
= 2
A square comes out to be a two-dimensional object, but it doesn’t work out so cleanly with the Sierpinski Triangle. When you divide the triangle into pieces whose sides are half the size of the original, you get three self-similar triangles, so the formula works out:
Log(3)
= Log(2)
≈ 1.58496
But how can this be possible? The picture of the triangle is two dimensional. But remember, this is only a depiction of the triangle. The real Sierpinski Triangle cannot be drawn because it is infinitely detailed. 3
Another interesting aspect of the Sierpinski Triangle is its creation. There are several ways of producing an image of the Sierpinski Triangle. The first and simplest method is by taking an equilateral triangle and connecting the midpoints to create four triangles with sides that are half the size of the original. Disregard the middle triangle and repeat these steps with the newly created three other triangles. The Sierpinski Triangle begins to appear.
Of course, this would only be a true Sierpinski Triangle if you were to repeat these steps an infinite number of times. So, realistically, this method only creates an image that resembles the Sierpinski Triangle.
The next method of Sierpinski Triangle creation is by using the Chaos Game. The Chaos Game is a method that uses randomly picked points to build an image of the triangle. To
There are no specific coordinates to map out the Triangle. You could give the coordinates surrounding the area like Bermuda, Miami, Florida, San Juan, and Puerto Rico, but the actual triangle cannot be so easily defined.
The Bermuda Triangle,also known as the Hoodoo Sea, the Devil's Triangle, the Limbo of the Lost, and the Twilight Zone, is a part of the ocean in which planes, ships, and people mysteriously seem to just disappear. It is an imaginary area shaped as a triangle. Which is located in the outer tip of Florida. Its been the biggest mystery of time because of the mysterious disappearances that have happened over time. “The term Bermuda Triangle was first used in an article written by Vincent H. Gaddis for Argosy magazine in 1964. In the article, Gaddis claimed that in this strange sea a number of ships and planes had disappeared without explanation. Gaddis wasn't the first one to come to this conclusion, either. As early as 1952, George X.
The Texas Triangle is formed by the three major cities; Houston, Dallas/Ft. Worth, and San Antonio. These cities are connected by a three major Interstates 45, 10, and Interstate 35. If you followed those main routes and drew a line on a map you would see the route to and from those cities forms an actual triangle.
In the beginning of the book Simon Sinek talks about an even that occurred in Afghanistan where a group small group of special operation forces were moving through some dense terrain with two A-10 Warthog overhead for protection. But as the forces continued through they were getting a bad feeling and they were not the only ones. One of the A-10 Warthog pilot, whose nickname was Johnny Bravo, started to sense this bad feeling as well but was blinded by the clouds behind him and had minimal communication with the other forces. So with this deep sense of bad feelings Johnny Bravo decided to head through the dense clouds in order to see what was going on and provide a sense of safety for those on the ground. As he was descending he heard the worst
Mathematics and art have always been closely related: Golden ratio, symmetry, proportion and geometry are elements in the art; not surprisingly, many great artists of history have been great mathematicians; they have been supported in mathematics to express reality with an artistic language. By definition geometry comes from the Greek: Ge = earth and Metron = measure. That is, it is the branch of mathematics that studies the measurement of the Earth that is concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. (Geometry. (2015).
Marijuana, bud, hash ,ganja, reefer, a drug of many names. What makes this plant so special? is it the health benefits,the economic value or is it the illegality of it ? Well whatever it may be, it has made a huge impact on california, three counties in specific Mendocino, Humboldt, and Trinity county also known as The Emerald Triangle.These three counties are the biggest marijuana producing counties in california and the United States. Marijuana accounts for up to Two-thirds of the economy of Mendocino.(Estimated to be over a $1 Billion dollar economy in mendocino alone).These three counties are built upon generations and generations of pot growers. The impact that Marijuana makes in the Emerald Triangle is immense with all the products needed to grow being bought from the community businesses growing the community's economy all while supporting the local people.
The first proven fact is true be cause they have evidence of a plane disappearing right outside of the triangle, Through all the cases of aircraft disappearing no debris has ever been found, many people who have been in the triangle have reported that their compass has stopped working once they’re in the triangle. No evidence of Malaysian Flight MH370 has ever been found, and the Lost City of Atlantis has never been found as of yet. Others believe it has something to do with Aliens, but this has not been proven. Scientists do believe that weather, like underwater hurricanes play a part in these disappearances. They also believe topography, current and methane gas can also be a cause. They thing the gas kill the passengers causing them to sink. It’s a fact that passengers who have survived the journey through this area have lost their memory or the
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds,
It was an average evening at the Cauldron Supermax Prison. Thousands of miles from land, this prison held the most dangerous criminals on the planet. One of those notorious criminals was Triangular the Triangle and his only prison friend Ryden May. Ryden started a conversation, “Tri, my man, when are we gonna escape.” Triangular the Triangle had no response just anger in his annoying friend. He just wished he could ditch him.
In this book, Gregg Braden merges the modern discoveries of nature’s patterns (fractals) with the ancient view of a cyclic universe.
After a bit of thinking, we realized that shapes that were a scale factor of another have the same number of bounces, so for this to work, you need to reduce the numbers as if they were a fraction. 9/6 would be reduced to 3/2. Using this, we were able to create a formula that works for everything as long as they are reduced. Here it is: N + X - 2.This works for all reduced
Holden, Stephen. “Love Triangle Sideshow, a Circus’s Main Attractionâ€. The New York Times. April 21, 2011.
The triangle has been used throughout the mystery schools around the world as a symbol for manifestation. Points one, two and three represents thoughts, actions and the goal. Once you connect the three points you form a triangle or the manifestation. All things follow this pattern of creation. If you want to become a world class swimmer it will take more than just clicking your heels together three times with positive thinking to obtain your dream. You also need to get in the water and swim, swim a lot.
The Bermuda Triangle covers almost 440,000 square miles of the Atlantic Ocean. An imaginary line that begins near Melbourne, Florida, extends south to Bermuda, and west to Puerto Rico before turning north to Florida, forms the Triangle. From 1972-1999, more than one hundred planes and ships have vanished into thin air. More than one thousand lives have been lost as well. One frightening aspect of this entire saga
At this point you might be asking yourself: what difference does the shape of triangles make in a triangulation and, as such, why do we care at all about Delaunay triangulations? Well, let us consider one of the most relevant application examples for the 21st century. We live in a digital age and use a multitude of electronic devices on a regular basis; much more often than people did back in 1934. Almost all electrical devices nowadays contain some electronic circuitry that controls their functioning. This circuitry is usually placed on printed circuit boards, which present us with the task of deciding where on those boards the individual components have to be placed and how they should be connected to each other (de Berg et al. 2008). Since many of the electronic components emit heat, we have to be able to place our components on the circuit board in a way that minimizes the overheating. It is difficult to predict if the overheating will cause an issue for a given component layout, so we have to either create a prototype of the particular board and test it before starting the mass production, or we could simply run a computer program to simulate this test much more efficiently. Needless to say, nowadays everyone usually picks the latter method.