The Ratio Detective
The LUMS Math Circle session on April 25, 2025, was not an ordinary one—it was a thrilling journey through the hidden mathematics behind everyday life and cutting-edge chemistry. Dr. Adnan Khan and Dr. Basit Yameen turned abstract concepts into unforgettable experiences, proving that ratios are the invisible force behind everything from our favorite drinks to life-saving medicines.
Dr. Adnan Khan: The Ratio Detective
Dr. Khan kicked off the session by challenging students with real-world puzzles where ratios held the key to solving them.
The Lemonade Challenge
He presented two lemonade mixtures with different ratios of lemon to water and asked, "Which one packs a stronger citrus punch?" Students debated passionately, some guessing based on intuition, while others crunched the numbers to find the answer.
Chemistry’s Sneaky Appearance
Just when everyone thought they had ratios figured out, Dr. Khan threw in a twist—a detour into the chem lab! He posed a problem where acid and water had to be mixed in a precise ratio to create a specific solution volume. "Mess this up," he joked, "and you might end up with a failed experiment or a very bad day."
The Painter’s Dilemma
Next, students became decorators, mixing two shades of pink paint with different red-to-white ratios. "Can you create a brand-new shade by blending these?" Dr. Khan asked. The room buzzed with ideas as students experimented with proportions to hit the perfect hue.
The Nutty Business Problem
Finally, they stepped into the shoes of a health food entrepreneur, tasked with pricing a nut mix using ingredients with varying costs. "How do you hit the target price without losing flavor or profits?" The challenge? Balance quality and cost using you guessed it ratios!
Then, Dr. Basit Took Over…
With the stage set, Dr. Basit Yameen transitioned from theory to action, revealing how ratios don’t just exist in textbooks “they drive chemical reactions”.
The Mystery of Vanishing Fever
He began with a personal story: "Last night, I had a fever. I took medicine, sweated it out, and—poof!—it was gone. But what really happened inside my body?" This simple question led to a deep dive into the chemistry of aspirin, from ancient willow bark remedies to modern labs producing 40,000 tons of it yearly.
The Science Behind the Synthesis
After revealing aspirin's chemical structure, Dr. Basit explained the theoretical foundations of the synthesis experiment. He detailed how different analytical methods like TLC and IR spectroscopy could detect whether the reaction was successful - setting the stage for hands-on lab work.
Cooking Up Aspirin
In the lab, students explored the exact ratio needed to synthesize aspirin from salicylic acid and acetyl chloride. "Too much of one, and the reaction fails. Too little, and you’re left with a useless mix," Dr. Basit explained. The precision of stoichiometry suddenly felt alive.
Chromatography: The Reaction Detective
Then came the highlight—Thin-Layer Chromatography (TLC). Students watched as solvents carried reaction components across plates, separating them like invisible ink revealing secrets. Calculating retention factors (Rf), they saw firsthand how math confirms whether a reaction succeeded.
IR Spectroscopy: The Molecule’s Secret Language
The session wrapped up with infrared spectroscopy, where molecules "speak" through absorption peaks. When the aspirin sample showed its signature carbonyl stretch at 1749 cm⁻¹, the room erupted in "Whoa!"—math had decoded chemistry’s hidden language.
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Why This Session Was Unforgettable
Math Became Magic: Ratios transformed from dull equations to the backbone of flavors, colors, and medicines.
Chemistry Came Alive: Students didn’t just learn—they saw reactions unfold and molecules "talk."
The Bigger Picture: The session proved that disciplines aren’t silos. Math and science weave together to shape our world.
Final Thought:
Next time you sip lemonade or take an aspirin, remember—you’re not just tasting or healing. You’re experiencing the power of ratios.
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Want More?
Try mixing your ratios at home (safely, of course!).
Ask: "Which other everyday things rely on hidden math?"
This wasn’t just a lecture. It was a backstage pass to how the universe works. And honestly? We’re all nerds for it.
Acknowledgments
We extend our deepest gratitude to Dr. Adnan Khan and Dr. Basit Yameen for their captivating fusion of mathematics and chemistry, transforming abstract concepts into an unforgettable learning adventure. Special thanks to Miss Noreen Sohail and Mr. Qamar Abbas for their invaluable support in orchestrating this session—your dedication behind the scenes made this interdisciplinary exploration possible. This collaboration between brilliant minds exemplifies how mentorship and teamwork can ignite scientific curiosity.
Here are some highlights from the event:
