How Many Circles Pass Through Two Given Points?
The impact of technology on education is often overstated. However, some applications of technology are unequivocally transformative in mathematics teaching.
The question “How many circles pass through two given points?” is a wonderful prompt for a geometry class. It’s simple, it provokes debate, it can be explored in a variety of ways, and it connects to many important geometric concepts. And in the end, it requires some imagination on the part of the student to truly comprehend the answer.
And after all that classroom work, it is so powerful and satisfying to see something like this.
A simple demonstration that elegantly captures the essence of the problem, and leads to new compelling questions. That shows students that mathematics is beautiful and inspiring. And that takes just a few moments to put together in Geogebra.
And what’s truly transformative is how easy it is to get students using technology to create their own mathematics like this! This is the real promise of technology.