The Pythagorean Theorem: Euclidean Geometry

Improved Essays
Johnny Martinez
Period 7th Pythagorean Theorem
The Pythagorean Theorem also known as Pythagoras’s theorem is a relation in Euclidean geometry that are the tree sides of a right triangle. It’s the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. The equation use for it is A squared plus B squared equals C squared.The Theorem relates the lengths of the three sides of any right triangle. The theorem is named after the ancient Greek. There is evidence that indicates that Pythagorean Theorem was well- known to the mathematicians of the first Babylonian Dynasty (20th to 16th centuries BC) which would have been over a thousand years before Pythagoras was born. People say that Pythagoras discovered the theorem at least fifteen hundred years before Pythagoras was born. But no one really knows when it was founded or discovered. The Pythagorean Theorem was known long before Pythagoras but he might have been the
…show more content…
But the formal definition is in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Its useful because if we know the lengths of the two sides of the right angled triangle then you could find the length of the third side but that only works on right angled triangles.
If anyone is going to use it then it would be a squared plus b squared equals c squared. The letter C is the longest side of the triangle and A, and B are the other two sides. The Pythagorean theorem is the statement that the sum of the two small squares equals the big one. The equation lets you to find the length of a side of a right triangle when they've given you the lengths for the other two sides, and going in the other direction, it lets you to determine if a triangle is a right triangle when they've given you the lengths for all three

Related Documents

  • Improved Essays

    Quadratic Functions Essay

    • 1468 Words
    • 6 Pages

    The following formula represents the quadratic formula:x=(-b±√(b^2-4ac))/2a After plugging each number to their corresponding term, it must first look like the following x=(-(-1)±√(〖(-1)〗^2-4(2)(2)))/(2(2))Next “-1” is multiplied by a negative which equals to a positive “1”. Moreover, the discriminant must be simplified and equal to √(1-16) which equals to √(-15). In math, a square root must never be negative, so an “i” which stands for imaginary number will replace the negative sign and cancel out the square root. Now the quadratic formula looks like the following: x=(1±√(-15))/(2(2)). Then, the denominator is simplified by multiplying “2” times “2” which equals to “4”.…

    • 1468 Words
    • 6 Pages
    Improved Essays
  • Improved Essays

    If the number of 1s is odd, then the even parity bit will have a value of 1, otherwise the parity bit will be 0. In the same manner, an odd parity bit is generated by counting the number of 1s. However, if the number of 1s is even, then the odd parity bit will have a value of 1, otherwise the parity bit will be 0 Example 6 – 23. Generate an even parity bit of the bit string 10101101. Solution: Since there are 5 1s, then the even parity bit will have a value of…

    • 727 Words
    • 3 Pages
    Improved Essays
  • Improved Essays

    THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point.…

    • 2362 Words
    • 10 Pages
    Improved Essays
  • Superior Essays

    Lens Equation Analysis

    • 1124 Words
    • 4 Pages

    This means that the tanθ is the same for each triangle; Tanθ=opp/adj=h_0/f=(-h_1)/(d_1-f) Where h_0 is the object height, f is the focal length, h1 is the image height, d0 is the object distance and d1 is the image distance For the triangle below the central axis a minus sign has been added. This is because both θ are assumed to be positive. However the image height is inverted and therefore negative so to keep both tanθ’s positive a minus sign has been added. The same operation done above can also be done for the similar triangles in figure 3. Tanθ^ '=h_0/d_0 =(-h_1)/d_1…

    • 1124 Words
    • 4 Pages
    Superior Essays
  • Improved Essays

    1. Descriptive analysis of RR% and GR% The mean is a measure of central tendency that obtained by dividing the sum of observed values by the number of observations, n. Data points can fall above, below, or even on the mean, it is widely considered a good estimate for predicting subsequent data points. . For the retention rate (RR %), the mean is 57.41 while it is 41.76 for GR%, the dependent variable. The minimum and maximum are basically the least and highest observed value.…

    • 1040 Words
    • 5 Pages
    Improved Essays
  • Improved Essays

    However, we can measure the size using Borel set that we define its measure as a length. From this length, we can simply generalize the set to become Lebesgue measure Borel measures on R, B(R) is the smallest σ-algebra that contains the open intervals of R as stated in Wikipedia (2016). The Borel measure on real number, R is the choice of Borel measure which assigns μ ((a,b])= b-a for every half-open interval (a,b]. Besides, Weir (1974) mentioned that a Borel measure is any measure μ defined on the σ-algebra of Borel…

    • 956 Words
    • 4 Pages
    Improved Essays
  • Improved Essays

    Golf Ball Experiment

    • 2043 Words
    • 9 Pages

    The circumference of the ball was measured to be 13.75cm. To find the radius of the ball, the circumference was substituted into the formula C=2흿r. The radius of the ball was 2.188 cm. To find the volume of the ball, the equation V=흿(4/3)r3 was used. The volume of the ball was determined as 43.89 cm3, which is the same as 43.89mL3.…

    • 2043 Words
    • 9 Pages
    Improved Essays
  • Improved Essays

    Ex-Touch Triangle Essay

    • 785 Words
    • 4 Pages

    Hence Ex-Touch triangle is the pedal’s triangle of with respect to Bevan point. Now let us find the area of Ex-Touch triangle, We are familiar with the result that “In any triangle cevian divides the triangle into two triangles whose ratio between the areas is equal to the ratio between corresponding bases”. So and it implies…

    • 785 Words
    • 4 Pages
    Improved Essays
  • Improved Essays

    in a similar manner to Hipparchus, Ptolemy innovated upon Hipparchus’ method by inscribing regular polygons inside a circle and calculating the resulting chords from each polygon. By combining this with a method to find the chord subtended by half the arc of a known chord, Ptolemy calculated chord lengths accurate to six decimal places [2]. Ptolemy and his predecessors already knew about the Pythagorean identity, sin^2⁡x+cos^2⁡x=1 expressed as chords of a circle instead of our modern notation. Ptolemy also knew the formulas for the sine of the sum of two angles and the law of sines expressed with chords…

    • 1004 Words
    • 5 Pages
    Improved Essays
  • Improved Essays

    The data emerges a powerful and concrete report. Recall, the percentages were ignored at the beginning for the equal expectancy of 50. Additionally, the calculation is done just the same as the Chi-Square of Goodness of Fit Testing but with assuming unequal expected. The process is similar the only difference is to include the correct percentages with the corresponding majors as indicated. Should an individual what to do the standard calculation one can do that my creating a frequency table.…

    • 799 Words
    • 4 Pages
    Improved Essays