1. Ping Pong

2. Ping pong is the game we play with our friends, maybe at tooker or Manzi or Barrett, we make our own rules for it.
The difference between ping pong and table tennis is, table tennis is a sport with a specific set of rules played in a professional setting, it is also a sport in the Olympics.

3. Our video

4. g(x) = -.0068x^2 + .071x + 71 g’(x)=-.0136x^2 + .071 (0,71)
(-31.8, 61.7)
Sydney’s curve
(100,10)
(-97,0)
g(x) = x^ x + 71
g’(x)=-.0136x^

5. Distance Nearest to the Origin
For example we have two points of the coordinate plane (0,0) and (3,4). We can plug the values to get a distance of 5. We get the formula from the Pythagoras theorem

6. hypotenuse =(dx2+dy2)^(½)=(1+(dy/dx)^(2))^(½)
The length of the Arc length of a curve can be found if we make the curve into infinitely small line segments and find the distance of each of the curves.
“Formula comes from approximating the curve by straight lines connecting successive points on the curve, using the Pythagorean Theorem to compute the lengths of these segments in terms of the change in xx and the change in yy. In one way of writing, which also provides a good heuristic for remembering the formula, if a small change in xx is dxdx and a small change in yy is dydy, then the length of the hypotenuse of the right triangle with base dxdx and altitude dydy is (by the Pythagorean theorem)”
hypotenuse =(dx2+dy2)^(½)=(1+(dy/dx)^(2))^(½)
Arc Length =

7. Arc Length = cm
Velocity = 4.9m/s
Vikas’s Curve
(0,44)
(100,20)
(-95,0)
f(x) = x^ x + 44
f’(x) = x
f’’(x) =

8. Surface Area of Ping-Pong Ball using Revolutions
Description: “A surface of revolution is a three-dimensional surface with circular cross sections. For these problems, you divide the surface into narrow circular bands, figure the surface area of a representative band, and then just add up the areas of all the bands as they approaches infinity to get the total surface area. A surface generated by revolving a function, y = f (x), about an axis has a surface area — between a and b — given by the following integral”:
Mathematical Representation:

9. Graphical Representation of Ping Pong Ball Surface Area
“Plotted below is the function f(x)= (4-x2)(½) (the positive curve of the circular base of the ping pong ball being revolved around the line y=0). On the right is a visual representation of a cross-section created by a secant line attached to the curve. On the left is the same cross section, this time as the number of secant lines approaches infinity-- creating an infinite number of cross sections”.

10. 1st Degree Taylor Polynomial (aka: Linear Approximation)
Description: A Taylor series is a way to approximate the value of a function by taking the sum of its derivatives at a given point. It is a series expansion around a point x=a known as the focal point. If x=0 then the series is called a Maclaurin series, a special case of the Taylor series. When using a 1st degree Taylor polynomial to approximate a function it is also known as Linear Approximation.
Mathematical Representation:

11. Linear Approximation of Vikas’s Curve @ x=-95
Equation of curve: f(x) = x^ x + 44
1st Derivative: f’(x) = x
1st Degree Taylor Polynomial x=-95): 1.935(10-7) (x+95)

12. Graphical Representation of Linear Approximation

13. Sandy’s curve
(0,55)
(100,20)
(-100,0)
h(x)= x^2 + .1x + 55

14. In mathematics, a Riemann sum is an approximation that takes the form of a combination of rectangles. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations.
Now that we know the definition of a Riemann sums let's apply it to ping pong

15. Area of the curve by riemann sums

19. Area between the curves - There are a few steps we need to follow to find the area between curves
Find the points where the curves intersect.
Make them your two end points in the integral
Subtract the lower arc from the upper one in the integral and integrate with the two end points

20. Area between Vikas’s and Sandy’s Curve

21. Here is the area between Sydney and Vikas’s curves

22. Works Cited
sections

23. Thank you