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Archive for the ‘GeoGebra’ Category

GeoGebra: Fixed Point Iteration: Newton-Raphson Method (Newton’s Method)

October 29th, 2013 1 comment

Newton-Raphson is an iterative numerical method for finding roots of equations.
xn+1 = x− f(xn)/f′(xn)

Click the image to link to GeoGebraTube

Designed principally for use with the MEI-OCR C3 Coursework on Numerical Methods

GeoGebra: Fixed Point Iteration: Rearrangement Method x=g(x)

October 29th, 2013 2 comments

Numerical method for finding roots of f(x) = 0, by rearranging to x = g(x) and iterating
xn+1 = g(xn)

Click the image to link to GeoGebraTube

Designed principally for use with the MEI-OCR C3 Coursework on Numerical Methods

Statistical Outliers Impossible in Small Samples

October 13th, 2013 2 comments

How many pieces of data are needed before it’s possible for one of them to be an Outlier?

Read more…

GeoGebra: Graphical Mortgage Repayment Calculator

November 8th, 2012 No comments
Click the animation to link to GeoGebraTube
(Opens in a new window/tab).

Click here to link to GeoGebraTube

Calculate monthly repayments based on the amount you are borrowing and over how many years you wish to repay it.
or
Calculate how many years it will take to repay your mortgage based on the amount you are borrowing and your monthly budget.

GeoGebra: Probability Venn Diagram with Proportional Regions

March 19th, 2012 No comments
Click the animation to link to GeoGebraTube
(Opens in a new window/tab).

In the latest version of this dynamic Venn diagram you have full control over the values of P(A), P(B) and P(AnB).

The orange area representing P(AnB) is dependent on the distance between the centres of the circles. But this distance is the solution of an equation that cannot be solved analytically, so the Newton-Raphson numerical method runs in the background with four iterations.

GeoGebra: The Binomial Expansion

February 11th, 2012 No comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

Fully interactive: A geometric representation of the binomial expansion

Control parameters a,b,n in the function f(x)=(a+bx)n
Also control the number of terms in the binomial expansion.

The applet shows the correct function (black) alongside the binomial expansion of the function (green).
It also clearly shows the bounds (x-values) for which the expansion is valid.

Read more…

GeoGebra: The Ultimate Projectiles Applet!

January 29th, 2012 No comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

User-friendly applet designed with perfection and aesthetics in mind.

Play with the checkboxes and X points. Those with a grounding in projectile mechanics will find it is self-explanatory.

You can select: angle of elevation OR range OR an airborne target, for any speed of projection and strength of gravity.
The applet shows the possible trajectories under the given constraints.
The applet also animates balls projected at the selected angle of elevation.

GeoGebra: Tangent Fields & Isoclines

January 29th, 2012 No comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

This applet displays tangent fields and coloured gradient fields for general solutions of explicitly defined 1st order ODE’s (i.e. dy/dx = …..)
It also displays the particular solution curve; you can set the boundary condition by dragging the blue point. [Euler’s numerical method is used with error correction]

The applet also shows isoclines where possible [dy/dx=f(x,y) must be polynomial in x and y]

GeoGebra: Binomial Distribution with Normal and Poisson Approximation

June 6th, 2011 4 comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

This applet is for visualising the Binomial Distribution, with control over n and p.

It also shows the Normal Approximation curve (and how this approximation breaks down for large or small p)
and it shows the Poisson Approximation curve (and how his approximation breaks down if there’s no positive skew)

You can show critical regions at either end by turning the bars red instead of green. The appropriate cumulative binomial probabilities are shown.