The Zero Story

Number Origami

“If I make a paper plane using a piece of paper, and then unfold it, you will be able to fold it exactly as I did because there is a memory of folding left in that piece of paper,” says Prof. Divakaran. But, complains Shraddha, this does not apply to Kanjeevaram sarees! Where she’s going, Shraddha won’t need a saree. A kimono will do just fine. Our friendly mathematics professor and his eager student journey to Japan in their quest to unravel numbers. Origami, the Japanese art of paper folding, is more than an aesthetic pursuit of hobbyists. It packs in its intricate folds many fascinating clues to understanding prime numbers and other mathematical concepts. Previously in this series, we visited ancient Greece, India, Egypt, and Babylon. Queue our past episodes and catch up on the playlist. Credits: Akshay Ramuhalli, Bijoy Venugopal, Bruce Lee Mani, Narayan Krishnaswamy, Prashant Vasudevan, Sananda Dasgupta, Seema Seth, Shraddha Gautam, Supriya Joshi and Velu Shankar Discover more: Article | Tree-maker algorithm: https://langorigami.com/article/treemaker/ [https://langorigami.com/article/treemaker/] Book | Thomas C Hull | Project Origami: Activities for Exploring Mathematics, Second Edition (AK Peters/CRC Recreational Mathematics Series) https://www.amazon.in/Project-Origami-Activities-Exploring-Mathematics/dp/1466567910 [https://www.amazon.in/Project-Origami-Activities-Exploring-Mathematics/dp/1466567910] Book | Thomas C Hull | Origametry: Mathematical Methods in Paper Folding https://www.amazon.in/Origametry-Mathematical-Methods-Paper-Folding/dp/1108478727 [https://www.amazon.in/Origametry-Mathematical-Methods-Paper-Folding/dp/1108478727] Article | Miura Folding - Applying Origami to Space Explorations https://www.ijpam.eu/contents/2012-79-2/8/8.pdf [https://www.ijpam.eu/contents/2012-79-2/8/8.pdf] YouTube video | DW News | The girl that became Hiroshima's icon for world peace - Sadako Sasaki and the 1000 paper cranes https://www.youtube.com/watch?v=FzIB4LkVtUE [https://www.youtube.com/watch?v=FzIB4LkVtUE] YouTube video: The Smithsonian Channel | Language without Numbers? https://www.youtube.com/watch?v=nDM8G5tuHF8 [https://www.youtube.com/watch?v=nDM8G5tuHF8] Article: Recursion And Human Thought - Why The Pirahã Don't Have Numbers | A Talk With Daniel L. Everett | The Edge https://www.edge.org/conversation/daniel_l_everett-recursion-and-human-thought [https://www.edge.org/conversation/daniel_l_everett-recursion-and-human-thought] Website | Mathigon.org [http://Mathigon.org] | Mathematical Origami https://mathigon.org/origami [https://mathigon.org/origami]

A Greek Trajectory

Ed Sheeran would have been very much at home among the ancient Greeks. Because they, too, were in love with the shape of…everything, actually. Shape. And area and volume. And angles. The ancient Greeks were on a quest for precise measurement and perfect shapes. If their architecture is anything to go by, they knew a thing or three about proportion. Using simple tools they measured to precision and constructed to perfection. What’s this got to do with math? For the Greeks, numbers were not abstract entities; they were tied to the measurement of geometric properties. If you could draw it, it existed. Probably why, as we discovered in Ep 2, it never occurred to them to think of zero. Journey back to the age of Pythagoras with Divakaran and Shraddha in this exciting episode. And tell us something: three episodes down, has Shraddha gotten better at math? Discover more: PDF | Dartmouth University | Greek Mathematical Symbols | https://math.dartmouth.edu/news-resources/computing/resources_general/latex_math_symbols.pdf [https://math.dartmouth.edu/news-resources/computing/resources_general/latex_math_symbols.pdf] YouTube | Ted-Ed - How many ways are there to prove the Pythagorean theorem? - Betty Fei | https://youtu.be/YompsDlEdtc [https://youtu.be/YompsDlEdtc] World History Encyclopedia | Article - Greek Mathematics | https://www.worldhistory.org/article/606/greek-mathematics/ [https://www.worldhistory.org/article/606/greek-mathematics/] Credits: Akshay Ramuhalli, Bijoy Venugopal, Bruce Lee Mani, Narayan Krishnaswamy, Prashant Vasudevan, Sananda Dasgupta, Seema Seth, Shraddha Gautam, Supriya Joshi, and Velu Shankar

The Zero Story

Remember that dreaded figure your teacher scrawled on the margin of your math test paper? It’s the hero of this episode. Our much-villainised zero has a fascinating history. The Babylonians, as we discovered in Episode 1 (Babylon), may have arrived at a placeholder for zero, but the actual symbol did not enter convention until the 7th century in the Indian subcontinent. It later became a foundational element of mathematical concepts during the Islamic Golden Age (the word algebra has Arabic roots). Later, it was adopted in Europe by Renaissance mathematicians. Long story short: Zero has come full circle. In this episode, Divakaran and Shraddha host you through the evolution of zero through the ages. Further reading: Book | Physics for Entertainment by Yakov Perelman: Read online at OpenLibrary.org [http://OpenLibrary.org] - https://urlis.net/pvzgqofb [https://urlis.net/pvzgqofb] Full text at Archive.org [http://Archive.org] - https://urlis.net/d68xu7po [https://urlis.net/d68xu7po] Charles Seife: ZERO : THE BIOGRAPHY OF A DANGEROUS IDEA Book | Amazon India: https://urlis.net/w050djz8 [https://urlis.net/w050djz8] YouTube | Full Audio Transcript: https://youtu.be/tgvd1zMtKt0 [https://youtu.be/tgvd1zMtKt0] Credits: Akshay Ramuhalli, Bijoy Venugopal, Bruce Lee Mani, Narayan Krishnaswamy, Prashant Vasudevan, Sananda Dasgupta, Seema Seth, Shraddha Gautam, Supriya Joshi and Velu Shankar

Babylon

Babylon, as the story goes, is where applied mathematics took baby steps. “What, really?!” asks Shraddha. Remember the place value system that makes it easy to represent small and large numbers? That originated in Babylon, according to historical records that show that Babylonians had independently discovered the place value system as early as 2000 BCE to 1900 BCE. That’s more than a millennium before other civilisations. Another fun fact: The number 60 played a significant role in Babylonian mathematics, says Prof. Divakaran. To find out why (and more), listen to this episode. Further Reading: Ifrah, Georges: The Universal History of Numbers - from prehistory to the invention of the computer, published by John Wiley & Sons. PDF available at Internet Archive: https://urlis.net/q26qdop1 [https://urlis.net/q26qdop1] Where on earth is Babylon? Read this National Geographic Education article to know more: https://urlis.net/q3uqcv18 [https://urlis.net/q3uqcv18] Credits: Akshay Ramuhalli, Bijoy Venugopal, Bruce Lee Mani, Narayan Krishnaswamy, Prashant Vasudevan, Sananda Dasgupta, Seema Seth, Shraddha Gautam, Supriya Joshi and Velu Shankar