In Geometry, the term construction refers to the ‘drawing’ of geometric objects such as lines and circles with only the use of compass and straightedge. Construction does not allow measurement of both lengths and angles. The earliest study of Geometry, particularly parts of Euclid’s Elements focused on “building” Geometry based on compass and straightedge construction. In the following discussion, we will refer to compass and straightedge construction as simply construction.
Compass and Straightedge
Using dynamic geometry software (DGS), we can extend construction to computers, tablets, and mobile phones. In this post, we will learn how to use GeoGebra to mimic construction. For those who do not know about GeoGebra yet, it is a free multi-platform mathematics software (not just a DGS) that can be used for teaching and learning mathematics. You may download it here and if you want to learn about it extensively, I have created numerous tutorials on how to use it here. » Read more
Three years ago, I wrote a post about Photomath, a software capable of scanning and solving equations using phone cameras. I haven’t used the software in a while, and recently discovered that it also has added a capability of graphing functions. It can now graph polynomial functions, rational functions, and trigonometric functions, exponential functions, and logarithmic functions. Recent improvements also allows solving for exponential equations, derivative, integrals, and limits.
Shown below are some examples. I scanned handwritten equations of functions and graph them.
To use Photomath, just open it, click the Camera icon and point to then expression or equation.
To view the graph, click the red rectangle containing the equation at the bottom of the screen.
Aside from the graph, the output also shows some important information about the function such as its x and y intercepts, domain, minima/maxima.
I think Photomath is a very good software that can be used for learning mathematics. Students can use this app to verify answers and also to explore graphs. Photomath is a free app and is both available on Android and iOS.
For iPhone users, the long wait is over. In case you missed it (I missed it actually), GeoGebra has released the GeoGebra Graphing Calculator for iPhones last December. I have only personally used the app for a week and I’m really satisfied with its performance and speed on my old iPhone 5.
image via GeoGebra blog
For those who have not tried GeoGebra, it is a free and open-source software for teaching mathematics. We have a lot of tutorials about it here which I’m going to update to the current version of GeoGebra this year.
GeoGebra is available for desktop computers, tablets, and Android phones. It comes on multiple platforms including Windows, Mac, and Linux. You can also install it in the Google Chrome app.