The British Father of Mathematical Analysis: Newton’s Binomial Theorem, Gravity, and the Decomposition of Light into Colors

In heaven, Archimedes, Pascal, and Newton are playing hide-and-seek. Archimedes is “it” and starts counting. Pascal runs off beyond the horizon, while Newton looks around, picks up a stick, draws a square with sides of 1 meter around himself, and stands inside the square. Archimedes finishes counting, opens his eyes, and sees Newton:

“I see Newton!”
“Oh no! Newton per square meter is Pascal!” Newton replies.

Following our mathematical journey to ancient Syracuse, where the science of levers, spirals, and infinity was born under Archimedes’ influence (https://news.bdpu.org.ua/arhimedova-syla-uyavy-yak-antychnyj-genij-zvazhuvav-svit-i-obchyslyuvav-neskinchennist/), we also explored the mathematical legacy of Fermat and Leibniz (more on this soon) and summarized ancient mathematics through an open interuniversity lecture “Three Titans of Ancient Greek Mathematics” (https://news.bdpu.org.ua/nauka-i-osvita-ne-zupynyayutsya-vidkryta-mizhuniversytetska-lekcziya-try-tytany-davnogreczkoyi-matematyky/).

Once again this semester, as part of the mathematical club activities at the Faculty of Physics, Mathematics, Computer Science and Technological Education of Berdiansk State Pedagogical University, a fascinating extended-format session was held dedicated to the scientific legacy of Isaac Newton—the genius who forever changed our understanding of the Universe. Participants, including 5 invited students from Berdiansk Gymnasium “Leader” along with their mathematics teacher Maria Vasylivna Yefimova, immersed themselves in the world of fluxions and mechanics, where mathematical formulas explain planetary motion, falling apples, and the dance of light rays.

Primary focus was placed on Newton’s revolutionary discoveries: the method of fluxions (the prototype of differential calculus) and Newton’s binomial theorem. Students learned how it opens doors to understanding infinite series and approximate calculations, and they learned to see the connection between abstract mathematical constructions and the physical phenomena that surround us daily. Participants observed how Newton, in describing motion, created a fundamentally new mathematical language – the language of change – which today underlies all modern physics and engineering.

The session demonstrated the incredible connection between pure mathematics and physical reality: the formula for the law of universal gravitation is not merely a set of symbols, but a key to understanding cosmic order, from satellite orbits to ocean tides, governed by the same mathematical principles they studied during the session.

Full version:
https://www.researchgate.net/publication/398117169_Britanskij_batko_matematicnogo_analizu_binom_Nutona_gravitacijna_vzaemodia_i_dispersia_svitla_The_British_Father_of_Mathematical_Analysis_Newton’s_Binomial_Theorem_Gravity_and_the_Decomposition_of_Lig