Good Morning! 🌞 Did you know that the average ballpoint pen can write approximately 50,000 words—about 100 pages of text?

US News

The ‘Impossible’ Proof

Last year, two Louisiana high school students, Ne’Kiya Jackson and Calcea Johnson, made national headlines when they demonstrated a groundbreaking trigonometric proof of Pythagoras' Theorem, a feat mathematicians had not accomplished in over 2,000 years. Their discovery, which earned their school a major grant and invitations to publish their findings, showcased their exceptional ingenuity and passion for mathematics. Now, the duo has further solidified their place in mathematical history by publishing a new paper in the American Mathematical Monthly on October 28, where they present nine additional proofs of the theorem using trigonometric principles.

Pythagoras’ Theorem, a cornerstone of geometry, states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides, expressed as a2+b2=c2a^2 + b^2 = c^2a2+b2=c2. While simple in form, proving the theorem without circular logic has long been a challenge. Jackson and Johnson’s innovative approach relied on the principles of trigonometry—specifically sine and cosine ratios in right triangles—to disentangle overlapping concepts that had historically obscured the field's potential. In their paper, they emphasize how conflated terminology in trigonometry can hinder understanding, likening it to interpreting a picture with overlapping images.

By clarifying these concepts, the teens devised a series of proofs that illuminate new ways to think about the theorem. Their work not only advances mathematics but also serves as an inspiration to young women, particularly women of color, pursuing STEM fields. “To have a paper published at such a young age — it’s really mind-blowing,” said Johnson, now an environmental engineering student at Louisiana State University. Their paper offers detailed insights into their methods, inviting readers to explore these groundbreaking ideas and further cementing their legacy as trailblazers in mathematics.

Culture

Anonymous $3.5M Gift

Children 12 and under can now visit the Milwaukee Art Museum (MAM) for free, thanks to a $3.5 million anonymous donation. The gift will fund an endowment dedicated to supporting child admission.

According to the museum, the donor shared memories of visiting the museum with their family and wanted to ensure similar experiences for future generations. "This gift demonstrates how philanthropy can create a lasting impact," said MAM chief development officer André Allaire.

The free admission includes access to exhibitions, collections, and youth and family programs. Current exhibits feature Acceleration of History by Robert Longo and a collection of woodblock prints by LaToya M. Hobbs. MAM Director Marcelle Polednik emphasized that the endowment will continue the museum’s long-standing commitment to free educational experiences for children.

Environment

Wildlife Photo Winners for 2024

The Nikon Comedy Wildlife Photography Awards, renowned as the funniest photography competition in the world, announced its 2024 winners, with Milko Marchetti's "Stuck Squirrel" taking the top honor. This year's contest saw a record-breaking 9,000 entries from professionals and amateurs alike, with Marchetti’s shot of a red squirrel caught in a hilariously awkward pose impressing judges and audiences alike. Captured during a split-second leap in Italy, the image has consistently drawn laughter at nature seminars, prompting Marchetti to enter it into the competition, where it triumphed amidst fierce competition among 45 finalists.

The competition was founded in 2015 by Paul Joynson-Hicks and Tom Sullam, both professional photographers and passionate conservationists to create a refreshing, fun, and free photography competition unlike any other, showcasing funny images of the earth’s most amazing wildlife and raising awareness about conservation.

As the over-all winner, Milko gets a once in a lifetime safari in the Masai Mara, Kenya, with Alex Walker’s Serian plus a photography bag.

There were 9 Category Winners, including this charming snap of a Mantis mediterranea from Spain, which won the Insect Category.

There were special mentions for the younger generation of emerging photographers including the winning shot of a frog that won the Nikon Young Photographer Award (for those under 25), with a close up of a frog smiling at the camera. Kingston Tam from Australia received a Z8 + 24-120mm kit from Nikon for their entry.

There were Highly Commended Winners too, like the owl and woodpecker (pictured, top) and this one of a flying squirrel in Japan looking like a boss.

To see more winners or to enter next year’s competition, visit the Comedy Wildlife Photo website.

Support Daily Upsider!

Help our mission to share positive, meaningful news! Your support keeps us going without the need to bombard you with annoying ads!

Mind Stretchers

⁉️ 

I hold the power to paint a smile,
Though I’m quiet, I speak with style.
I wear down with every kiss,
What am I, do you guess this?

Answers to yesterday’s Mind Stretchers

I travel far, yet stay in one place.
I bear the marks of every race.
Though I’m worn, I never complain,
I’m your silent partner through sun and rain.
What am I? — shoes! No one got this correct yesterday 🌞 

Be the first to send us the correct answer for today’s mind stretcher for a shout-out with the answer tomorrow. Just send us the answer and your name to [email protected] or reply to the email.

If you have any uplifting stories and experience you might want to share, send those over to [email protected] for the chance to be featured.