A Mathematical Blog

In this post, I will be talking about a few ways of constructing a triangle in Geogebra - an online graphing calculator. What method or methods you will be using to construct a triangle will depend on what parameters you know for that triangle.  Using Polygon Tool Probably the easiest way is by using the tool named Polygon , it is located under the heading ‘Polygons’ in the Shapes menu.  Select this tool simply by left click of a mouse or a single tap on screen. To draw a triangle using this tool, just click any three different spots on the graph to mark the locations of the vertices of a triangle with points. Click again on the first point you made to finish constructing the three sides figure.  Normally, i would use the Polygon tool when i just want to put down any random triangle without caring about its side lengths or angle measures or its location in the coordinate system. But suppose we want a triangle at a specific location in the coordinate system. Let’...

In this post, I will be writing about how to plot or mark points in Geogebra - an online graphing calculator. So let’s begin straightaway.  I will be talking about plotting points in a 2D graphing calculator(there is a 3D equivalent too).  Geogebra has many tools that help us to construct points in different examples. The basic tool to draw a point is the Point tool found under the heading ‘Basic Tools’ in the Shapes menu. It can also be located under the heading ‘Points’.  We will select this tool by simply clicking on it. Its name will be blued and in bold after its selection. Once selected, we can mark a point anywhere on the graph with a simple left click of the mouse or a single tap on screen.  Now the obvious drawback is that the Point tool is not a good choice of selection for accurate evaluations. Say you want a point to appear at exactly the coordinates (1.83, 2.79). In such cases where we want to pinpoint the point, we could simply type in the...

In two dimensions, a pair of lines can be any one of either intersecting or parallel. But in three dimensional space there is a third alternative. A pair of lines in 3D can be skew lines.  A pair of lines that do not intersect and are not parallel either are characterised as skew lines. And that’s the only way to describe them. Skew lines are straight lines in 3D that are neither pointing in the same two directions nor cutting through each other .  We can always find a plane in 3D that contains two intersecting lines. Same is true for a pair of parallel lines as well. But skew lines can never be both in the same plane.  But for a given pair of skew lines we can always find a unique pair of parallel planes each containing one of the two lines. This is an important property which helps us derive the formula for finding the shortest distance between two skew lines - a topic studied in 3D geometry.  But first, what is the shortest distance between two lines?...