(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 means they are Pythagorean triples. Rule 〖side〗_1^2+〖side〗_2^2=〖hyp〗^2
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]
Around Two thousand five hundred years ago, a Greek mathematician, Pythagoras, invented the Pythagorean Theorem. The Theorem was related to the length of each side of a right-angled triangle. In a right-angled triangle, the square on the hypotenuse, the side opposite to the right angle, equals to the sum of the squares on the other two sides. (148, Poskitt) To know more about this famous theorem, we can look at the other forms of the Pythagorean Theorem, such as it can also be written as c^2-a^2=b^2
Pythagoras, a man who is immortalized through his genius in the field of mathematics, or more specifically and more widely known the Pythagoras Theorem. A revolutionary theorem, which he created alone, which allows one to uncover the length of the missing side of a triangle by utilizing the other two sides. However, this theorem was not the only thing that Pythagoras was remembered for. In fact he is remembered for his philosophies, childhood, secret life and society, and influential adventures.
Pythagoras was a mathematician who has influenced the math culture until this day. His studies in math are more noted than his contributions to philosophy as well as religion. Due to the fact Pythagoras lived between roughly 520-495 bc there is very little information about him. In fact his exact birthday and death date are mainly estimations based on other historical events. Whatever we know about him is information learned after his death. Most of his writings were not published so we do not
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
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
important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship for areas of similar figures. Did Pythagoras derive the Pythagorean Theorem or
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
Intro to Glue Blocks Typical stairs consist of two basic components a tread, horizontal, and a riser, vertical. However, over time stairs begin to degrade causing slight warping in the trend. This shrinkage of the wood as well as weaken of the fastener between the riser and trend causes the two components to rub together, this creates an unpleasant squeaking sound. To solve these problems, a joint called a “glue block” is used with nails or screws to secure the joint to the underside of the trend
for sine (opposite divided by the hypotenuse), cosine (adjacent divided by the hypotenuse), and tangent (opposite divided by adjacent). This method can also only be used with right triangles. When doing a problem like this, it will state which method you should use (sine, cosine, or tangent). Let's start with sine first. Sine is listed above as OPPOSITE ÷ HYPOTENUSE. The side corresponding with the 90-degree angle (the only angle given) is always the hypotenuse of the triangle. The angle you are
theorem, and calculate primitive Pythagorean triples with one odd and one even number. The theorem is called by di erent names: Pythagoras' theorem, the hypotenuse theorem or Euclid I 47, so called because it is listed as Proposition 47 in Book I of Euclid's Elements. The theorem states that in a right-angled triangle, the area of the square on the hypotenuse, the side opposite the right angle, is equal to the sum of the areas of the squares on the other two sides.
To begin to understand the mathematics behind building a bridge we need find out the different types of a bridges. The definition of a bridge is a structure carrying a road, path, or railroad across a geographic obstacle. There are three different types of bridges. They are: beam/arch bridges, suspension bridges, and truss bridges. Modern beam bridges usually span up to 200 feet, modern arch bridges can span across 800-1,000 feet, while Suspension bridges can span from 2,000-7,000 feet ("HowStuffWorks")
i got this from a geometry book Theorem 1-1 Vertical Angles Theorem Vertical angles are congruent. Theorem 1-2 Congruent Supplements Theorem If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent. 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
equivalent to the law of cosines. Pythagorean Theorem Pythagorean Theorem is a relationship of the length of three sides of a triangle containing a right angle and is often written as a² + b² = c². It states that “The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides" , which can be shown as the picture below. In the picture, the blue area, which is the area of square C, is equal to the red area, which is the sum of
three basic ratios of trigonometry. What these ratios mean; Tangent = Opposite/Adjacent Sine = Opposite/Hypotenuse Cosine =Adjacent/Hypotenuse In the case of using trigonometry to work out the height of the eucalyptus tree, we only need to use the tangent ratio in our formula because we have length of adjacent and we need to find the opposite length and the tangent ratio is opposite/hypotenuse. The formula itself is; Tan(θ) x adjacent = opposite. So using this formula but with the data we collected
Trigonometry Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclicalphenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation
Investigating Free-falling Objects and Projectile Motions Aim: The aim of my experiment is to obtain results/ data and see whether a pattern can be distinguished or whether my data agrees with a theory or law. I'm going to try to undergo two investigations using the same apparatus, and look at the outcome of my results and see whether a firm conclusion can be made. For the two investigations, I'm going to look at free-falling objects and projectile motions: Investigation 1:
basic trigonometric functions are sine, cosecant, cosine, secant, tangent, and cotangent. In a right triangle, the sine of an angle is the opposite side from the angle divided by the hypotenuse of the triangle. Cosecant is its reciprocal. The cosine of an angle is the side adjacent to the angle divided by the hypotenuse. Secant is its reciprocal. The tangent of an angle is the side opposite of the angle divided by the side adjacent to the angle. Cotangent is its reciprocal (“The Six Trigonometric Functions
Bloodstain pattern analysis (BPA) is the interpretation of bloodstains at a crime scene in order to recreate the actions that caused the bloodshed. Analysts examine the size, shape, distribution, and location of the bloodstains to decide what happened. BPA uses biology (behavior of blood), physics (cohesion, surface tension, and velocity) and mathematics (geometry, distance, and angle) to assist investigators in answering questions like: • From where did the blood originate from? • What was the cause