PDF for mathematics from the official Punjab Board website. Access chapter-wise details for mathematics with the link to download the PDF, and more to plan your studies effectively ...

Dr. James McCaffrey from Microsoft Research presents a complete end-to-end demonstration of computing a matrix inverse using the Newton iteration algorithm. Compared to other algorithms, Newton ...

Once all are solved, the individual proofs are combined by DeepSeek-V3's informal thought chain to construct a proof of the original complex theorem.

Welcome to the edge of reality, where technology has officially started showing off. We've discovered 24 gadgets that make us seriously question whether someone's been secretly time traveling or ...

NPR's Ailsa Chang talks with Regina Barber and Emily Kwong of Short Wave about the oldest known tadpole, new proofs of the Pythagorean Theorem, and the evolutionary roots of alcohol consumption.

Two US college students discovered five new proofs of Pythagoras' theorem using trigonometry, expanding the theorem's understanding in a published study.

Two High Schoolers Found an ‘Impossible’ Proof for a 2,000-Year-Old Math Rule—Then, They Discovered Nine More Ne’Kiya Jackson and Calcea Johnson of Louisiana published a new study proving ...

Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.

Ne’Kiya Jackson and Calcea Johnson have published 10 trigonometric proofs of the Pythagorean theorem, a feat thought impossible for 2,000 years.

Teenagers Publish Trigonometric Proof Of Pythagoras’ Theorem Once Considered Impossible Calcea Johnson and Ne'Kiya Jackson have added four further novel proofs of the theorem that had also not ...

Teens who made history with Pythagoras' theorem discovery publish their first academic paper with new proofs Date: October 28, 2024 Source: Taylor & Francis Group Summary: In their peer-reviewed ...