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Math Apps in Maple

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Example: Drawing the Graph of a Quadratic Function

The following example allows the student to learn how to draw the graph of a quadratic equation (a parabola).

Generate a quadratic function and try to draw it on the graph. Use the radio buttons below the graph to graph different elements in different colors. When you are finished, click the corresponding check boxes to see how accurate you were.

f(x)=

Show:

Draw:

 

Example: Epicycloids and Hypocycloids

This next app allows the student to user sliders, buttons and checkboxes to adjust the parameters of an epicycloid, hypocycloid, epitrochoid or hypotrochoid, the equations for which are given by:

 

x(theta) = (R+r)*cos(theta)+s*L*r*cos((R+r)*theta/r)

y(theta) = (R+r)*sin(theta)-L*r*sin((R+r)*theta/r)

The curve is called an epicycloid when s = 1 and L = 1; a hypocycloid when s = -1 and L = 1; an epitrochoid when s = 1 and L <> 1; and a hyptrochoid when s = -1 and L <> 1.

The figure can also be animated by clicking on the "Play" button.

Fixed circle radius (R) =

Rolling circle radius (r) = 

Start End

Ratio (L) of Pen length/radius

Example: The Monkey and the Coconut

The following classic thought experiment, The Monkey and the Coconut is used to illustrate the effect of the gravitational force on a projectile.

 

A coconut tree is growing in the middle of a small river. Two monkeys arrive at the bank and notice a small ripe coconut about to fall into the river. In order to get the coconut, the monkeys make a plan: On the count of three, the first monkey will shake the tree, while the other will jump across the river and catch the coconut as it falls, landing on the far bank.

 

How should the second monkey aim her jump in order to catch the coconut?

 

Adjust the monkey's initial speed and jump angle so that she catches the coconut.

Jump angle =

Speed=

Note: Air resistance is negligible, and time has been slowed down.

Example: Monte Carlo Approximation of Pi

This example from Statistics shows how to use the probabilistic Monte Carlo method to estimate the value of Pi:

 

1. 

A number of points are selected at random within a square with an inscribed circle

2. 

The number of points inside the circle divided by the total number of points will result in an approximation of π/4. We multiply by 4 to get the estimate for Pi.

 

Adjust the number of points being plotted and see how it affects the approximation of Pi.

number of dots=

 

Legal Notice: © Maplesoft, a division of Waterloo Maple Inc. 2012. Maplesoft and Maple are trademarks of Waterloo Maple Inc. This application may contain errors and Maplesoft is not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact Maplesoft for permission if you wish to use this application in for-profit activities.