Category: High School Geometry

3D Math Applets Galore at Maths.Net

High School Geometry, High School Mathematics

Last year, I have shared about an applet for visualizing isometric views. I found another superb 3d math applets site,  Maths.Net, through Great Maths Teaching Ideas. Maths.net includes applets for exploring prisms, nets, platonic solids, and other 3-dimensional objects. It also includes an applet for building polyhedra.

My favorite applet is Guess the view. It lets guess the isometric view of a particular solid.

It turned out that the applets in Maths.Net are also from Wisweb, the same site where I discovered the isometric views applet.

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Using Paper Folding to Introduce the Notion of Proof

High School Geometry, High School Mathematics

Two years ago, I worked as part-time geometry instructor in a technical school near our university.  Most of the students in that school were quite clueless about the notion of proofs, so I tried to find ways to introduce proofs in an intuitive manner.

One lesson I developed was on proving that a quadrilateral formed from paper folding is a square.  I let the students create a square from a piece of bond paper without using any measuring instrument; only folding and cutting were allowed.

proof

As expected, most of the students used the method shown in the figure above. For the sake of discussion, we label the corners and critical points of the bond paper.  Most of the students constructed the square using the following steps (see figure): » Read more

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Diagonals of a Parallelogram

High School Geometry, High School Mathematics

Coordinate geometry was one of the greatest inventions in mathematics.  Aside from connecting geometry and algebra, it has made many geometric proofs short and easy.  In the example below, we use coordinate geometry to prove that the diagonals of a parallelogram bisect each other.

The proof can be simplified by placing a vertex of the parallelogram at the origin and one side coinciding with the x-axis.  If we let a and b be the side lengths of the parallelogram and c as its altitude, then, the coordinates of the vertices can be easily determined as shown below.

In addition, if we label the vertices P, Q, R, and S starting from the origin and going clockwise, then the coordinates of the vertices are P(0,0), Q(b,c), R(a + b,c) and S(a,0). » Read more

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