Category Archives: STEM

Pole Dancing with the Stars

A few years ago I received this photo from my cousin, Doug, who at the time was living at Casey Station, Antarctica. Doug is a communications technician with the Australian Antarctic Division. Over the past decade he has mostly lived and worked at one or another of the four A.A.D. research bases. This year he is at Macquarie Island. He sends a weekly newsletter, adorned with magnificent photos of pristine icy landscapes, extraordinary wildlife and colourful and mind-blowing captures of the night sky that include Aroura Australis and time-lapse star-trails like the photograph here.

I find all his stories and photography amazing, but the mathematician in me drew special interest in this South Pole time-lapse specimen. There is no set point in the picture that identifies exactly where the south celestial pole (SCP) lies, but it’s not too difficult to pose a guess when considering the circle centre from all these arcs. The arcs themselves are quite interesting, because they are the actual stars, with their movement recorded over a slice of time. From our perspective, it would seem that any given star would complete a full circle around the SCP in 24 hours. However, we know that what’s really rotating is our Earth against the fixed background of stars. Here then comes the obvious maths problem: For how long was the camera shutter open in order to take this photo?

Here’s how I did it:

  1. I started by importing the photo to a Graphs page of my TI-Nspire CAS.
  2. I then moved the axes to place the origin at where I estimated the SCP to be.
  3. Next I selected one of the star-trails. You can see that my selection is towards the lower-left of the photo, but really any of them would do.
  4. I graphed f1(x)=1 and then used the line-rotation feature until the line ran across one end of the star-trail arc (blue line).
  5. I graphed f2(x)=1 and used the line-rotation feature again until the line ran across the other end of the star-trail arc (red line).
  6. The CAS indicates the equations of the two lines and I extracted the gradient of each into a Notes page.
  7. Continuing on the Notes page I used the two gradients and a known formula to compute the angle of the arc. (Note that my document is set to degrees)
  8. This angle as a fraction of 360 degrees equates to the exposure time as a fraction of a full day. I have made my calculation of the exposure time in seconds further down the Notes page. (1593 s in this example – about 26.5 mins)
Photograph credit: Doug McVeigh. Australian Antarctic Division, Casey Station 2015

And now the best part of it all: I can check my result another way! Remember that my cousin Doug had sent me this digital photo, which as a JPG file, I can not only view it, import it into calculator software, but I also have the original metadata. Here is the details page for the file. Note that among bountiful information, the exposure time is indicated: 1652 s. My calculation was but 59 s out.  

Want to see more classroom resources from the deep south? Classroom Antarctica is a comprehensive online teaching resource produced by the Australian Antarctic Division, with lesson plans aimed at grades 3 to 8. Ideas contained in Classroom Antarctica will stimulate your students’ interest in real-world applications for science, mathematics and studies of society and environment, inspiring and engaging your students in learning.

TI industry partner for MAV Maths Camp

Twenty-four enterprising Year 10 students made the selection for this year’s STEM-focused MAV Maths Camp held in the first week of July this year. Texas Instruments joined the program as a new industry partner this year and hosted all students for a site visit on the Wednesday. Students were provided an insight into the tasks of TI team members and particularly where STEM skills & knowledge are called upon. This was especially emphasised in a video conference meeting with Harshal S Chhaya from TI’s product development team in Dallas, Texas. Harshal discussed his STEM roles within TI and students had an opportunity to ask questions about task specifics and career path options.

Harshal remarked, “I was glad to interact with these students and talk to them about my work as an engineer. They were very curious to learn about TI. I was also impressed by the questions on the importance of ethics in technology”

Following this, all students had an opportunity to work with the TI-Innovator and completed an RGB activity. Most then worked on TI-Rover activities under the guidance of Peter Fox, while T-Cubed Trainers, Shelley Cross and Karleigh Nicholls mentored a focus group.

Other industry partners for the program were Ford, Reserve Bank of Australia, RMIT University and Victorian Space Science Education Centre. Over the week, all students visited each of these industry sites for a general overview. Additionally, student teams of 4 or 5 were partnered with each of the industries to be mentored through deeper research into a particular problem or project.

The TI project team, mentored by Shelley and Karleigh, investigated the problem of pets being left in hot cars (Pet Alarm Project) and presented their product and findings to the MAV (Mathematics Association of Victoria), mentors, teachers and fellow students at the end of the week. Along the way, this group completed 10 Minutes of Code activities, researched how the colour of the car can affect the internal temperature of a car and the biological effects of heat to different dog sizes. They completed the Pet Alarm project successfully by building their individuals cars, coding the TI-Innovator to flash LED lights, sound an alarm and using the servo motor open the car windows.

T-Cubed Manager, Daisy Patsias, commented:

“It was truly wonderful to see how excited they all were with their final product. Mentors Karleigh Nicholls & Shelley Cross did a wonderful job of working with these students throughout the week. They even provided the students with extension questions to investigate before their group presentations that were held at the end of the week. Peter Fox also did a wonderful job with the balance students working with TI-Rover. The students really loved this experience. The TI mentor group presented a wonderful report to the whole group about their project. They also showed one of the cars demonstrating how when the temperature reached 26 degrees the alarmed was activated.”

“In fact it was during the group’s presentation to their peers that I really saw how much they got out of the Pet Alarm project. I was very impressed with their presentation and their explanation of all STEM associations with in the project.

Overall there was a lot of work involved both prior to the event and during the event week but seeing what the students got out the program was very rewarding. It is easy to see how such a program can be life changing to Students.”

The Happy Rover – Girls in STEM Day

As the focus on STEM continues to gain momentum, so also did TI-Rover when it was put to the test by over 200 girls who attended a Girls in STEM day that was held recently at Ivanhoe Girls Grammar (9 Aug 2019). Hosted by the Mathematical Association of Victoria and attracting sponsorship from Ford, Texas Instruments, Engineers Without Borders, Aurecon and others, the successful event is now in its third year.

True to the theme of ‘Inspired by Curiosity’ the girls were receptive to presentations from GHD Group, SORA Architecture, Quantum Market Research, and the Bureau of Meteorology. Following morning tea and a panel discussion, the girls were given their chance for real hands-on STEM-task engagement in a two-part activity challenge that was facilitated by Texas Instruments and Engineers Without Borders.

Accredited T3 Instructors Shelly Cross and Karleigh Nicholls, from St Hildas School on the Gold Coast, led the TI component which assigned students the task of coding TI-Rover to race against other Rovers from fellow student teams; forward to a finish line, turn around and then return to the start line. Delighted T3 Manager, Daisy Patsias, observed “The girls were very engaged and loved ‘playing’ with TI-Rover. Presenters Shelly and Karleigh as always did a fabulous job and the girls appeared to love the activity. There was a lot of competitive spirit displayed on the day.”

Racecam video can be viewed at: https://youtu.be/M4BbVomPrU4