Light Year and the Mathematics of the Stars

Last week, we have talked about large numbers and one million. In this post, we will talk about some of the practical uses of large numbers.

One of the uses of large numbers is to measure long distances; for instance, distance between celestial objects. Shown below is a table of the distances of the planets from the sun and from earth rounded off to the nearest thousand kilometers. Giving a speed of a commercial airline (approximately 500 kilometers per hour), a trip from Earth to Venus will require us 10 years of travel while traveling to Pluto will require us 1,306 years. Shocked?

*By the way, Pluto has recently been demoted. Recent updates made it clear that it does not qualify being one of the planets. » Read more

GeoGebra Essentials 6 – Sliders and Rhombuses

This is the sixth tutorial in the GeoGebra Essentials Series. If you are not familiar with GeoGebra, you may want to read the Introduction to GeoGebra post and earlier tutorials. They contain the pre-requisites of this tutorial.

In the tutorial below, menu commands, located in the menu bar, are in brown bold text, and submenus are denoted by the > symbol. For example, Options>Labeling> New Points Only means, click the Options menu, choose Labeling from the list, then select New Points Only. The tool texts are colored orange. For example, New Pointmeans the new point tool.

In this tutorial, we construct a rhombus using the slider tool.  A slider (see figure below) is a dynamic graphical representation of a number.  We have three types of sliders – number, angle and integer.  The angle and number sliders are shown below. Slider s is the side length of the rhombus ABCB’. Slider t on the other hand is the measure of angle A.

In doing the tutorial, we  learn the following:

  • Use the tools we have discussed in previous tutorials – Segment tool, Parallel Line tool,and Intersect tool
  • Learn how to use new tools including Angle with Given Size and Segment with Given Length from Point . » Read more

WordPress Blogging Tutorial 2 – Typing Your First Blog Draft

Before we post our first blog, let us first familiarize ourselves with the environment of WordPress. The Dashboard (Figure 1) is the environment where we will always work . The Right Now panel contains the number of Posts, Pages, Categories, Tags, and Themes. The QuickPress panel will enable us to publish short posts quickly.

Figure 1

Below the window are different panels: Recent Comments, Recent Drafts, Stats and others. Do not be overwhelmed by these panels; we will use each of them as we go on. For now, we will concentrate on the basics. Try to familiarize yourself with the environment.

In our first post, we will copy the post Proof of the Pythagorean Theorem in my cousin’s blog Polymath Central (Figure 2).  As we can see, we will need the two pictures of right triangles. You can go to the blog and download them before proceeding. Those pictures came from one of my posts; you are permitted to use them in your blog for the sake of this tutorial. Of course, you can create your own first blog if you wish. » Read more

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