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.
I have shared several decent calculators and graphing tools in this blog, but in this post, I’m going to share the calculators that I actually use nowadays. The calculators I use depend on the task that I’m doing. I use my phone for short and simple calculations, but if I’m studying or working for an hour or more, I use an actual calculator to avoid distractions. Here are the four calculators that I use most of the time.
1.) Calculator (Mac)
When I’m using my laptop, I use the default calculator app of MacOS. This app allows the user to choose among basic, scientific, and programmable modes. It also supports base 8, base 10, and base 16 number systems. Personally, I only use the basic and scientific calculators and I have not tried the programmable calculator yet.
2.) Google’s Calculator App (Android)
Google’s calculator is a simple and beautifully designed app for basic calculations and scientific calculations. It can store previous calculations. I like the simplicity of this app, so I use it most of the time for basic calculations when I’m using my Android phone. This app is compatible with WearOS.
3.) Advanced Calculator FX991 (Android). This is a paid app but I really like it because it mimics the interface of an actual calculator (see image below). I’ve been using it for six months and so far, I really liked it.
4.) Casio FX991 ES Plus. Aside from apps, I also keep a Casio 991ES Plus. It’s not that I wanted to buy this calculator, but it was the only decent calculator in a store the time when I wanted to buy one. So far, so good, I’ve gotten used to it. I think I will be using it for a long time.
That’s all. Maybe you can share the calculators that you’re using in the comment section below.