February 11th, 2012
Micky
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…
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]
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.
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)
You can show critical regions at either end by turning the bars red instead of green – this feature is purely for visualising critical regions when performing hypothesis tests with the binomial distribution (you still have to calculate the critical regions yourself). I hope to automate this too in a future version of the applet.
1. From the WordPress Dashboard, install a plugin that enables iframes to be embedded into posts, for example Embed Iframe. (Simple instructions for installing plugins into WordPress may be found here) Read more…
When taking square roots of both sides of an equation, one should be careful not to turf out the negative result without first considering whether it has a true meaning. When using Pythagoras’ Theorem, the last step is to take square roots. So, can we have a hypotenuse with length -5?
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The original motivation behind this was an attempt to save my Statistics students a few precious seconds in their upcoming S1 module paper.
The mean or expectation of a Binomial Distribution is always very close to mode or the value of X that has greatest probability. I want to know if you can use the mean to reliably predict the mode.
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September 2nd, 2010
Micky
There are plenty more where this one came from. Although this is the only one that swears. The others dance, and when I’ve done a bit more research on the Parametric B-Function (discovered through serendipity) I shall blog the findings.
This is made from a quintic graph (a polynomial of degree 5). It’s possible to apply the Parametric B-Function to any y=f(x) graph, including reciprocal, hyperbolic and trigonometric functions. I’m determined to find a practical use for the function. I’m thinking music. Watch this space. Read more…
1. Imagine a cuboid made up of lots of little cubes.
2. Imagine a straight line (or “traversal”) connecting two opposite vertices of the cuboid
3. How many little cubes does the line pass through?
Note: Cubes are only counted if the traversal passes through them, so if your traversal goes exactly through a vertex or an edge separating cubes within the cuboid, then it is not considered to pass through the adjacent cubes. In the 2×3×4 example shown, the traversal actually passes through an edge in the centre of the cuboid.
Problem: How many cubes does a traversal pass through in a 60×120×156 cuboid? (Hint: Start small!)
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- Draw a rectangle on squared paper.
- Draw a diagonal across your rectangle.
- How many squares does it pass through?
Note: If your diagonal goes exactly through a point, like in the 2×4 example, then it is not considered to pass through either of the diagonally adjacent squares.
Problem: How many squares does a diagonal pass through in a 190×884 rectangle?b
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