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
Waclaw Sierpinski Waclaw Franciszek Sierpinski was born March 14, 1882 in the capital city of Warsaw, Poland. He attended school in Warsaw where his talent for mathematics was quickly spotted by his first mathematics teacher. This was the phase of Russian occupation of Poland and it was a complicated time for the talented Sierpinski to be educated in Poland. The Russians had enforced their language and culture on the people in Poland in sweeping changes to all secondary schools implemented between
the ones that capture all my attention and interest. For example, while working with the Sierpinski Triangle at the Johns Hopkins Center for Talented Youth geometry camp, I was struck with a strong determination to figure out the secret to the pattern. According to the Oxford Dictionary, the Sierpinski Triangle is “a fractal based on a triangle with four equal triangles inscribed in it. The central triangle is removed and each of the other three treated as the original was, and so on, creating an
Beyond Pythagoras - Mathematical Investigation 1) Do both 5, 12, 13 and 7, 24, 25 satisfy a similar condition of : (Smallest number)² + (Middle Number)² = (Largest Number) ² ? 5, 12, 13 Smallest number 5² = 5 x 5 = 25 Middle Number 12² = 12 x 12 = 144+ 169 Largest Number 13² = 13 x 13 = 169 7, 24, 25 Smallest number 7² = 7 x 7 = 49 Middle Number 24² = 24 x 24 = 576+ 625 Largest Number 25² = 25 x 25 = 625 Yes, each set of numbers does satisfy the condition.
what a perfect being is, than God must be a sovereign being. Similar to his triangle theory that it is not a necessity to imagine a triangle. It is not a necessity to imagine a perfect being rather a thought that has run through our mind. The triangle as imagined and conceived has three sides and a hundred and eighty degree angles as always. It is imperative that these characteristics are always attributed to the triangle, likewise the attributes of a perfect being are placed on God. In order to prove
How far does imaginary numbers go back in history? First must know that an imaginary number is a number that is expressed in terms of the square root of a negative number. This fact took several centuries of convincing for certain mathematicians to believe, but imaginary numbers have been used all the back to the first century, and is now being widely used by people all around the world to this day. It is thanks to people like Heron of Alexandria, Girolamo Cardano, Rafael Bombelli, and other mathematician’s
find the area of irregular triangles and a regular triangle, irregular quadrilaterals and a regular square, this will prove whether irregular polygons are larger that regular polygons. Area of an isosceles irregular triangle: ======================================== (Note: I found there is not a right angle triangle with the perimeter of exactly 1000m, the closest I got to it is on the results table below.) To find the area of an isosceles triangle I will need to use the formula
fitting 4 triangles inside each triangular surface of an icosahedron; which is one of the five solids created by the ancient Greeks. When considering a icosahedron, or any regular polyhedral for that matter, we have the following formulas to consider: 1. V = 10υ2 + 2 2. F = 20υ2 3. E =
Using Tangrams To Explore Mathematical Concepts Representations have always been a very important part of teaching mathematics. The visuals and hands on experiences help to aide the teachers by assisting them in relaying important topics and concepts to the students. By having a representation, the students are more likely to remember what they have learned, and recall the lesson when it comes time to take a test or do their homework. Within mathematics, many different manipulatives are
area when using 1000 meters of fencing, was a square with the measurement of 250m x 250m and the area=62500m² Isosceles Triangles I am now going to look at different size Isosceles triangles to find which one has the biggest area. I am going to use Pythagoras Theorem to find the height of the triangle. Pythagoras Theorem: a²=b²+c² Formula To Find A Triangles Area: ½ x base x height 1. Base=100m Sides=450m [IMAGE] [IMAGE] a²=b²+c² 450²=b²+50² 202500=b²+2500
Drain Pipes Shape Investigation Introduction A builder has a sheet of plastic measuring 2m by 50cm, which he uses to make drains. The semi-circle is the best shape for a drain. Prove this. I will prove this by comparing its volume to that of other shapes. On older houses there are semi-circular drains but on newer houses there is fancier ones like pentagon shapes. Is this because they are better or is it simply for design? To find the volume of a 3D object I have to find the
perimeter of 1000 metres of fencing. I then worked out the areas of each shape using known mathematical formulae and techniques such as Pythagoras' theorem to calculate the sides of right angled triangles; using trigonometrical functions (sine, tangent and cosine) to calculate either angles or sides of triangles constructed. Sometimes there are no known exact formulae for working out the area of certain shapes such as octagon and more complex polygons. In such cases, given shapes are split into shapes
race? I would like to investigate two different models one being a right-angled triangle and the other being isosceles triangle. When investigating the isosceles triangle, an equilateral triangle would be investigated because as the length of the isosceles triangle will all equal, it becomes an equilateral triangle. I would first of all investigate the right-angled triangle. Model 1: Right-Angled Triangle C [IMAGE] A B [IMAGE] PREVAILLING CURRENT AT A SPEED OF 2 MS-1 [IMAGE]
The Triangle Between Othello, Iago, and Cassio I chose to look at the triangle between Othello , Iago, and Cassio because these three men are very important in the play. They are important to each other and the people around them. The relationship between the three of them is very strange because someone is always trying to get back at the other one and they don’t care about each others feelings or anyone else’s. In the end this leads to a blood shed fight. Othello is the main character, heÕs the
Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know little about his achievements. There is nothing that is truly accurate pertaining to Pythagoras's writings. Today Pythagoras is certainly a mysterious figure. Little is known of Pythagoras's childhood. Pythagoras's father was Mnesarchus, and his mother was Pythais. Mnesarchus was a merchant who came from Tyre. Pythais was a native of Samos. As a
Theorem 1-3 Congruent Complements Theorem If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent. Theorem 2-1 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Theorem 2-2 Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Theorem 2-3 Polygon Interior Angle-Sum Theorem The sum of the measures of the interior angles of an
Physics problems can be solved and worked through many different ways. For example, for the second half of the problem (when we used d = d0 + v0t + ½ at2), we could have also used trigonometry to find the height, since we already know the base of the triangle (half the distance) and the angle. Despite enrolling late and still trying to figure everything out, I still participated in the class a bit, having asked and answered a few questions of Piazza. For example, I helped another newly enrolled student
Applications of Trignometry Trigonometry is the branch of mathematics that is based on the study of triangles. This study helps defining the relations between the different angle measures of a triangle with the lengths of their sides. Trigonometry functions such as sine, cosine, and tangent, and their reciprocals are used to find the unknown parts of a triangle. Laws of sines and cosines are the most common applications of trigonometry that we have used in our pre-calculus class. Historically. Trigonometry
And these tablets are believed to date about 1000 years before Pythagoras. And the Babylonians are not the only ones!According to Eric McCullough & Brian Deitz the Egyptians knew that a triangle with sides 3, 4, and 5 make a 90 degrees angle, and they also used a rope with 12 evenly spaced knots that they used to build perfect corners in their buildings and pyramids. In another article, titled The History of the Pythagorean Theorem, ancient
sides and angles of a triangle, such as Special Right Triangles (30, 60, 90 and 45, 45, 90), SOHCAHTOA, and the Law of Sines and Cosines. These methods are very helpful. I will explain how to use all three of them with examples at the end. The first example, Special Right Triangles, is used only with right triangles. To use this method, you need to have angle measures of 30, 60, and 90, or 45, 45, and 90. There is a "stencil" that goes with these degrees. In the 30-60-90 triangle, the side opposite