MATHEMATICS

  Irrational Numbers An  Irrational Number  is a real number that  cannot  be written as a simple fraction:   1.5  is rational, but  π  is irrational Irrational means  not Rational  (no ratio) Let's look at what makes a number rational or irrational ... Rational Numbers A  Rational  Number  can  be written as a  Ratio  of two integers (ie a simple fraction). Example:  1.5  is rational, because it can be written as the ratio  3/2 Example:  7  is rational, because it can be written as the ratio  7/1 Example  0.333...  (3 repeating) is also rational, because it can be written as the ratio  1/3   Irrational Numbers But some numbers  cannot  be written as a ratio of two integers ... ...they are called  Irrational Numbers . Example:  π   (Pi)  is a famous irrational number. π  = 3.1415926535897932384626433832795... (and more) We  cannot  write down a simple fraction that equals Pi. The popular approximation of  22 / 7  = 3.1428571428571... is close but  not accurate . Another clue is tha

  Pi ( π )   Draw a circle with a  diameter  (all the way across the circle) of  1 Then the  circumference  (all the way around the circle) is  3.14159265...  a number known as  Pi   Pi  (pronounced like "pie") is often written using the greek symbol  π The definition of  π  is: The  Circumference divided by the  Diameter of a Circle. The circumference divided by the diameter of a circle is always  π , no matter how large or small the circle is!   To help you remember what  π  is ... just draw this diagram. Finding Pi Yourself Draw a circle, or use something circular like a plate. Measure around the edge (the  circumference ): I got  82 cm Measure across the circle (the  diameter ): I got  26 cm Divide: 82 cm / 26 cm = 3.1538... That is pretty close to  π . Maybe if I measured more accurately? Using Pi We can use  π  to find a Circumference when we know the Diameter Circumference =  π  × Diameter Example: You walk around a circle which has a diameter of 100 m, how far have yo

  The Pentagram The Pentagram (or Pentangle) looks like a 5-pointed star. You may think it has something to do with witchcraft, but in fact it is more famous as a  magical symbol  and is also a holy symbol in many religions. In fact, this simple figure is quite amazing. Inside a Pentagram is a Penta gon   You can make a pentagram by first drawing a  pentagon , then extending the edges.   Or by drawing lines from corner to corner inside a pentagon. Polygon In fact a Pentagram is a special type of  polygon  called a "star polygon".   Ratios The regular pentagram has a special number hidden inside called the  Golden Ratio , which equals  approximately 1.618 a/b = 1.618... b/c = 1.618... c/d = 1.618... When I drew this, I measured the 4 lengths and I got a=216, b=133, c=82, d=51. So let's check to see what the ratios are: 216/133 = 1.624... 133/82 = 1.622... 82/51 = 1.608... If I had drawn and measured more accurately, I would have been even closer! Why not have a go yourself

  What are Trigonometric Identities? Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.  There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. The trigonometric identities hold true only for the  right-angle triangle . All the trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the  sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. All the fundamental trigonometric identities are derived from the six trigonometric ratios. List of Trigonometric Identities There are various identities in trigonometry which are used to solve many trigonometric problems. Using these trigonometric identities or formulas, complex trigonometric questions can be solved quickly. Let us s

  What Is a Graph? Math and numbers can be hard to understand, especially if you have a lot of data you are comparing. However, a graph can make it easier. Why? Because a graph is data or numbers put into an easy-to-follow picture. And depending on the type of numbers you are working on graphing; you might need a different type of graph for each. For example, if you were comparing different color shirts in your classroom, you might use a bar graph or pie chart. However, if you want to connect numbers in a line, you might use a line graph. Graphs vs. Charts While you might hear  chart  and  graph  used interchangeably, these two terms are not exactly the same. Graphs are types of charts. Charts are a way to present information graphically, including graphs, diagrams, tables, and other visual representations of data. So while all graphs are charts, not all charts are graphs. Since that’s confusing, it might be easier to remember that visual representations of math relationships are found