Discovery of the Cartesian Plane
Our latest session, led by the dynamic duo Dr. Qasim Imtiaz and Dr. Imran Anwar took us on a thrilling journey through the realm of relative rates! and its versatile applications to various phenomena in real life. Physics, ecology, urban growth, and environmental concerns are a few examples where the session showed how relative rates connect diverse phenomena through mathematics.
We began with a fascinating tale of Rene Descartes' discovery of the Cartesian Plane, connecting algebra and geometry. Our young mathematicians then embarked on a treasure hunt, navigating the Cartesian Plane to grasp the concept of relative rates.
Next, we delved into Galileo's genius experiments, exploring gravity and relative rates through captivating video clips. Using Galileo’s principle, the session debunked common misconceptions about falling objects. Participants analyzed how air resistance influences lighter and heavier objects, deepening their understanding of relative rates of acceleration due to gravity. This segment provided a blend of theoretical insight and practical examples, encouraging critical thinking. We even witnessed falling objects in a vacuum chamber accelerating simultaneously!
But that's not all! Our participants applied relative rates to real-world problems, including:
The population growth rate of Lahore city (verified using UN data): is a very basic example of relative rates, but still so empowering because based on this data the government officials have to prepare the basic needs for the upcoming year. This practical example highlighted the importance of understanding relative rates in city planning and resource allocation.
The Pizza Problem: optimizing pizza quantity relative to radius
Participants then addressed the Pizza Problem, a fun yet mathematically rich challenge focused on maximizing the amount of pizza in comparison to its radius. Analyzing the relationship between the radius and the area, the group discussed how even a very small increase in the radius yields huge gains in pizza size. This problem made the relevance of relative rates to everyday choices clear.
In building on the earlier ecological theme, the participants explored a method of estimating dolphin populations in the deep ocean using relative rates. They discussed how the tagging and re-sighting techniques, or mark-and-recapture models, depend on proportionality to estimate large populations from smaller sample observations. This applied example highlighted the use of mathematics in wildlife conservation.
Drug concentration in blood
The session also explored the dynamics of drug concentration in the bloodstream over time. Participants examined how rates of absorption and elimination determine the drug’s effectiveness and safety. This problem illustrated the critical role of relative rates in pharmacology and healthcare.
Carbon dioxide growth rate in the air
In the session’s highlight, participants discussed the alarming rise of carbon dioxide levels in the atmosphere. The group examined the role of human activity in accelerating greenhouse gas accumulation by comparing annual emission rates with absorption capacities. This problem underscored the urgent need for sustainable practices and policies.
Engagement and Takeaways
Throughout the session, participants engaged in activities like solving problems, discussing implications, and sharing insights. Tying abstract concepts to real-world examples during the session fostered an appreciation of the role of mathematics in diverse fields.
Acknowledgments
Heartfelt thanks to Dr. Qasim Imtiaz and Dr. Imran Anwar for delivering an unforgettable session that captivated and inspired participants. This enriching event was brought to life through the collaborative efforts of the LUMS Mathematics Department and the unwavering organizational support of Ms. Noreen Sohail, Mr. Qamar Hussain, and Mr. Javaid Qayyum. Together, their dedication and expertise ensured a seamless and impactful experience for all.
Here are some highlights from the event:
