# IntMath Newsletter: Vectors activity, GeoGebra 5

By Murray Bourne, 28 Nov 2014

28 Nov 2014

In this Newsletter:

1. Math in cross-wind landing vectors applet

2. GeoGebra 5 now with 3-D graphs

3. Math puzzles

4. Final thought - thank you

## 1. Math in cross-wind landing vectors applet

I recently updated the crosswind landing applet in the Vectors chapter, so it now runs on tablets.

There is some interesting math behind this cross wind landing applet. Let's take a look at it: |

## 2. GeoGebra 5 now with 3-D graphs

GeoGebra is a great tool for exploring math concepts in a visual way. It is a powerful free graphing tool that allows you to develop your own interactive math applets, with no coding knowledge required (well, a little helps!).

I've been looking forward to the release of version 5 for some time, as it promised 3D graphics. It came out a few months ago and I've been having a play with it recently.

One of the early drawbacks of GeoGebra was that it worked on desktops only (being Java-based). But now it can be used on iOS, Android and Windows tablets, and as for phones, they say it's "coming soon".

GeoGebra's latest version offers 3D graphs and output that can be viewed on tablet devices. Here's a quick overview with some graph examples. |

## 3. Math puzzles

The puzzle in the last IntMath Newsletter asked about cup capacity when mixing gasoline and oil. The correct answer with explanation was given by Chris, Rajat and Nicos.

**New math puzzle**: What is the value of *e*^{ln x}? How does it differ from the value of ln *e*^{x}?

(**Note:** "ln" is the natural logarithm, and "ln *x*" means "log* _{e}x*". I've always thought the notation for natural logarithm is terrible, and I complain about it when introducing natural logs.)

Leave your responses here.

## 4. Final thought - thank you

Yesterday was Thanksgiving in the USA. In line with this topic, one of my most popular recent tweets was:

Education is a wonderful blessing, but sadly, it often seems to be appreciated only by those who don't have easy access to it.

Until next time, enjoy whatever you learn.

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