Investigation I am doing an investigation to look at shapes made up of other shapes (starting with triangles, then going on squares and hexagons. I will try to find the relationship between the perimeter (in cm), dots enclosed and the amount of shapes (i.e. triangles etc.) used to make a shape. From this, I will try to find a formula linking P (perimeter), D (dots enclosed) and T (number of triangles used to make a shape). Later on in this investigation T will be substituted for Q (squares) and
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
Triangles: Scalene [IMAGE] The diagram above is not to scale. Instead of having the perimeter to 1000m, only in this diagram, I have made the perimeters of the shape to 10, only to make this part of the investigation easier to understand. We know that the base of all the shapes is 2. The lengths for the equilateral triangle are 4 on each side. This part of the investigation is to explain why the triangle with the longest height cannot have the same base. The tallest triangle also
Their Areas The objective of this coursework is to find out which shapes have the biggest area. The perimeter must be 1000m, and the shapes can be regular or irregular. First of all I will experiment with different rectangles, the different triangles, then pentagons. Then I will experiment with more regular shapes (or whatever type of shape has the largest area) to see the effect on area changing the number of sides has. I predict that the largest shape will be a regular circle, and the more
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
Triangles seem like complex shape to understand although they happen to be the most simple shapes in geometry because, they come in many different varieties such as, equilateral (3 equal sides; 3 equal angles always 60 degrees), isosceles (only 2 equal sides;2 equal angles), and scalene (no equal sides; no equal angles). Triangles also come in a variety of angles, acute (all angles are less than 90 degrees), right (has a right angle) , and obtuse ( has an angle more than 90 degrees). A triangle is
is because it is very slow and tedious to do the work by hand. However, some simple fractals such as a Koch curve or a Sierpinsky triangle can be created by hand. The Koch curve for example starts out as a straight line. Then, in the middle of the line, an equilateral triangle is formed. From that point, every straight line becomes split by an equilateral triangle. This step would be repeated over and over until a snowflake forms. The result of repeating the process five times is shown below
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
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]
Math Fencing Project I have to find the maximum area for a given perimeter (1000m) in this project. I am going to start examining the rectangle because it is by far the easiest shape to work with and is used lots in places (most things use rectangles for design- basic cube .etc). To start with what type of rectangle gives the best result. A regular square or an irregular oblong? I start by having 4 individual squares. [IMAGE] [IMAGE] [IMAGE] [IMAGE] [IMAGE][IMAGE]
the distance of one side of a right angle triangle, (usually known as either a, b and c or side1, side2 and side3) fit the rule a2 + b2 = c2 then the combination of those numbers is a Pythagorean triple. The concept is only correct when the triangle used is a right angle triangle because there must be a hypotenuse across from the right angle. The demonstration used consists of three triangles each of them use positive integers, are right angle triangles and they all fit the rule a2 + b2 = c2, which
Mathematics contributes to everyday life in some way or another. Some situations are simpler than others. Someone may just have to use simple addition or subtraction in paying his or her bills. Or someone may even have to use more complex math like solving for a missing variable in an equation to figure out the dimensions of a building. Mathematics will always be used in everyday life. Some theories and algorithms are more important or used more often than others. Many mathematicians have developed
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
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
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