In this episode of Flashcards Friday at Math! Science! History! Gabrielle Birchak unzips the fascinating world of packing problems, the mathematical puzzles behind fitting everything into your suitcase. Discover how optimization theory and combinatorial math are at play every time you pack, ship, or store something efficiently. Whether you're prepping for vacation or running a tech company, the same mathematical rules apply.

3 Take-aways! (Pun intended!)

1. What packing problems are and why they matter in math, logistics, and data storage.

2. Why packing problems are so difficult, and why your perfect suitcase is more impressive than it seems.

3. How optimization techniques like sorting, rotating, and greedy filling are used in real-world applications, and how to apply them to your next trip.

Resources & Further Reading

Math for Liberal Studies: Bin-Packing Algorithms

Solving Hard Problems with Heuristics: A Beginner’s Guide

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Long before telescopes and satellites, Hipparchus of Nicaea looked to the skies and changed the course of scientific history. In this fascinating episode of Math Science History, Gabrielle revisits the life and legacy of the ancient astronomer whose innovations in trigonometry, geography, and star mapping still resonate today. From discovering axial precession to laying the groundwork for the astrolabe, Hipparchus helped humanity understand our place in the cosmos: mathematically, geographically, and philosophically.

Three Key Take-Aways

How Hipparchus measured the Earth's axial precession and why this was a monumental scientific discovery.

The mathematical brilliance behind his trigonometric tables and how they informed tools like the astrolabe.

How ancient astronomy evolved into cartography, influencing how we view geography and time today.

Resources & References

Griffith Observatory Astronomers Monument: https://griffithobservatory.org

Ptolemy's Almagest: Loeb Classical Library

Hipparchus in The Internet Encyclopedia of Philosophy: https://iep.utm.edu/hipparchus/

Cosimo Bartoli’s Del modo di misurare: https://archive.org/details/delmododimisurar00bart

🔗 Explore more on our website: mathsciencehistory.com
📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

🌍 Let’s Connect!

Website: mathsciencehistory.com
Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social
Instagram: https://www.instagram.com/math.science.history

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If you love Math, Science, History, here’s how you can help:
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🎵 Music: All music is public domain and has no Copyright and no rights reserved.
Selections from The Little Prince by Lloyd Rodgers

Until next time, carpe diem!

Episode Overview:

What do black holes, a teenage genius, and a long ocean voyage have in common? In this Flashcard Friday episode of Math, Science, History, Gabrielle tells the incredible story of Subrahmanyan Chandrasekhar, who, at just 19 years old, sailed from India to England and made a discovery that would transform astrophysics forever.

Armed only with a notebook and fresh ideas from quantum mechanics, Chandrasekhar calculated the limit of stellar collapse, now called the Chandrasekhar Limit, which revealed when a star collapses into a black hole. This isn't just a story about equations; it's a story about persistence, quiet genius, and the power of taking a break.

3 Things You'll Learn in This Episode:

1. What the Chandrasekhar Limit is and why it's essential for understanding black holes

2. How quantum mechanics, relativity, and statistical math came together to predict the death of stars

3. Why slowing down and giving your mind time to wander can lead to world-changing discoveries

Resources:

NASA: Black Holes Explained

Biography of Subrahmanyan Chandrasekhar – NobelPrize.org

A. S. Eddington and Chandrasekhar Controversy – arXiv

Chandrasekhar’s Original 1931 Paper (PDF)

Explore more on our website: mathsciencehistory.com
To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

Let’s Connect!

www.Instagram.com/math.science.history

https://bsky.app/profile/mathsciencehistory.bsky.social

https://www.linkedin.com/company/math-science-history/

https://www.threads.com/@math.science.history

Enjoying the Podcast?

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Leave a review – It helps more people discover the show!
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Checking out our merch: https://www.mathsciencehistory.com/the-store

Music: All music is public domain and has no Copyright and no rights reserved.
On Matters of Consequence from The Little Prince by Lloyd Rodgers

Until next time, carpe diem!

Episode Overview

Once dismissed as mathematical absurdities, black holes are now recognized as real, powerful features of our universe—cosmic wells where space, time, and even light collapse. In this episode of Math! Science! History!, we explore the astonishing story of how black holes evolved from a rejected theory to an accepted reality. From Einstein’s reluctance and Oppenheimer’s overlooked models, to John Wheeler’s advocacy and Stephen Hawking’s revolutionary radiation theory, this episode traces the full arc of scientific discovery—and what black holes reveal about our own place in the cosmos.

Three Key Take-Aways

Why Karl Schwarzschild’s World War I-era math predicted black holes decades before anyone took them seriously

How John Wheeler changed the game by naming—and championing—the black hole

What modern observations like Cygnus X-1, Hawking radiation, and LIGO’s gravitational wave detection tell us about collapsed stars and spacetime

Resources & References (the books include affiliate links)

Oppenheimer & Snyder (1939): On Continued Gravitational Contraction

David Finkelstein (1958): Past-Future Asymmetry of the Gravitational Field

Kip Thorne’s book: Black Holes and Time Warps: Einstein’s Outrageous Legacy

Marcia Bartusiak’s book: Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved

LIGO and gravitational wave discovery (2015)

🔗 Explore more on our website: mathsciencehistory.com
📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

🌍 Let’s Connect!

Website: mathsciencehistory.com
Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social
Instagram: https://www.instagram.com/math.science.history

🎧 Enjoying the Podcast?

If you love Math, Science, History, here’s how you can help:
🌟 Leave a review! It helps more people discover the show!
📢 Share this episode with friends & fellow history buffs!
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☕ Support the Show: Coffee!! PayPal

🛍 Check out our merch: https://www.mathsciencehistory.com/the-store

🎵 Music: All music is public domain and has no Copyright and no rights reserved.
Selections from The Little Prince by Lloyd Rodgers
🎵 Audio: Podcast mixed by David Aviles

Until next time, carpe diem!

In this Flashcard Friday episode, Gabrielle dives into the surprising history and science of sunblock. From ancient Egypt’s jasmine oils to modern SPF 50 sprays, discover how sunscreen evolved and why it’s one of the best defenses against deadly melanoma. Gabrielle shares the statistics on skin cancer, explains how sunblock works, and gives you simple tips to stay protected. With her favorite motto, “Just say NO to melanoma,” she’ll leave you ready to face the sun smartly.

3 Things Listeners Will Learn:

- The fascinating history of sunblock, from ancient remedies to modern formulations.

- How sunscreen protects the skin and how to use it correctly for maximum safety.

- Eye-opening facts about melanoma risk, survival rates, and prevention through sun protection.

Resource Links

American Cancer Society: Melanoma Skin Cancer Overview

All About Sunscreen: Why You Need It. How it Works for You

Melanoma Treatment (PDQ®)–Patient Version

Visit us!

Explore more on our website: mathsciencehistory.com

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www.Instagram.com/math.science.history

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https://www.threads.com/@math.science.history

Enjoying the Podcast?

If you love Math, Science, History, here’s how you can help:
Leave a review – It helps more people discover the show!
Share this episode with friends & fellow history buffs!
Subscribe on your favorite podcast platform

Checking out our merch: https://www.mathsciencehistory.com/the-store

Music: All music is public domain and has no Copyright and no rights reserved.
On Matters of Consequence from The Little Prince by Lloyd Rodgers

Until next time, carpe diem!