Sierpinski triangle

shapes. A polyhedron is a three dimensional object composed of flat polygon sides typically connected at the edges (Wolfram 1999). The most common shape of modern soccer balls is called a truncated icosahedron. Icosahedron is a shape made up of 20 triangles. To create a more round object the icosahedron is truncated. Here, truncated applies to cutting off the edges which makes the icosahedron look more round ("Icosahedron," 2014). The truncated icosahedron has 32 total faces including 12 regular pentagons

The building was created as a triangle since it would require less material and would be quicker to create than building a four sided building. The building stayed the same height through the sections and we felt that that would be the most stable since the building would be able to

examined several different methods, I was confused as to how a person could think of such strategies. This method was first derived by Bhaskara. I used this proof, because it best connects with the crime scene situation at hand. The use of multiple triangles and squares mimic the makeup of a room. Bhaskara’s Proof: I decided to manipulate Bhaskara’s method and make it more understandable for my usage. My interpretation

appealing which requires proportion, balance, and conjunction with its surroundings. This report looks at architecture and how trigonometry and mathematics have been used in developing St. Peter’s Basilica and the Pantheon through sectors and right triangle trigonometry. St. Peter’s Basilica is a late Renaissance church located in Vatican City built at the place of crucifixion of St. Peter the Emperor Constantine at request of pope St. Slyvester I. It was originally built from 315 A.D. – 349 A.D. but

advanced geometric constructions such as creating an equilateral triangle and a regular hexagon. I grasped the techniques quickly, and used my leisurely hours to practice. Many of the sheets of paper in my binder consist of perpendicular line bisectors, or angle copies. One eventful day, my geometry educator passed out a blank piece of paper, and told us to construct a square. Earlier in the week, we had learned to make an equilateral triangle and a regular hexagon. Prior to that lesson, we ascertained

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

Compass and Straightedge: Basic Constructions and Limitations In Euclid’s Elements, Book 1, the very first proposition states, “To construct an equilateral triangle on a given finite straight-line.” (Heiberg, Fitzpatrick, Euclid, pg 8) This proposition is saying that it is possible to construct an equilateral triangle from a given segment. Euclid was able to perform this construction with just a straightedge and compass. As The Elements was published in 300 BC (Heiberg, Fitzpatrick, Euclid, pg 4)

To identify a Special Right Triangle. The angle measure must be known first. If the given angle measure is 45°-45°-90° Special Right Triangle. Also if the given angle measure is a 30° or a 60°. Then the triangle is a 30°-60-°-90° Special Right Triangle In a 45°-45°-90° triangle. There are two legs and a hypotenuse. The hypotenuse is opposite the 90° angle. The legs are opposite the 45° angles. Since the two legs are of equal length. When given the length of one. The other leg always have

As a mathematician, he is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics.[5][6] As an astronomer, he composed a calendar which proved to be a more accurate computation of time than that proposed five centuries later by Pope Gregory XIII.[7]:659[8] Omar was born in Nishapur, in northeastern Iran. He spent most of his life near the court of the Karakhanid and Seljuq rulers in the period which witnessed

“the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero, if the following number is always added to the previous as shown below, a triangular number will always be the outcome: 1 = 1 2 + 1 = 3 3 + (2 + 1) = 6 4 + (1 + 2 + 3) = 10 5 + (1 + 2 + 3 + 4) = 15 Moreover, triangular numbers can be seen in other mathematical theories, such as Pascal’s triangle, as shown in the diagram