### Archive

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)

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

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

## GeoGebra: Graphical Mortgage Repayment Calculator

##### Click the animation to link to GeoGebraTube (Opens in a new window/tab).

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

##### 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

##### 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.

## GeoGebra: The Ultimate Projectiles Applet!

##### 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

##### 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]