At the end of my previous blog entry, I suggested that the mathematics involved in how the Equation of Time is determined by summing two sine curves (each from the variation of 'sun' time due to the earth's tilt and elliptical orbit) could prove a fruitful area of research for a student exploration in the new internal assessment program for Math HL & SL.

It reminded me that one of the better extended essays in mathematics that I've seen was about the mathematics in how a sundial works and how to make a sundial.  I think this would also be a worthwhile topic for which a student could write an exploration (internal assessment).

The sundial was arguably the first time measurement tool invented by humans.  The earth's rotation is fairly stable which makes it a useful basis for a clock.  A sundial - by means of casting a shadow onto some scaled measuring plate - tries to mirror this rotation.  As stated in the previous entry, this kind of 'sun' clock will run fast or slow depending upon the time of the year due to the effects caused by the earth's tilt and elliptical orbit.  The variation caused by each of these effects can be expressed as trigonometric functions.

But I digress, my main point here is that I would definitely have the topic of sundials on any list of potential exploration (IA) topics that I give to my students.  Yes, I think that a useful ingredient in the management of the new internal assessment program (exploration) is to provide students with a list of ideas for exploration topics.  I think that this will prove a more effective and efficient way to get students started in the initial phase of the IA program - when they need to choose a suitable topic to research and on which they will write an exploration.  This will be the most important and possibly the trickiest stage of the whole process.  This is discussed in some detail in the IA (Exploration) section of this site.

Let me finish with a couple of good internet resources on sundials and the mathematics of sundials:
Sundials on the Internet - a good list of sundial sites
The Mathematics of Sundials - a paper (2001) from the mathematics dept of the National University of Singapore (also 30 websites listed on the references page)
... and for a nice brief introduction to sundials the Open University (UK) has a 90 second video entitled The Sundial as a Mathematical