# Mathematicians Have Discovered the Secret Geometry of Life

From the spirals of shells to the layout of cells, a new class of shapes redefines nature’s complexity.

• Mathematicians show “soft cell” shapes are abundant in natural world.
• Soft cells are described as natural tiles with curved edges—a stark contrast to the mathematical solutions for creating tiling shapes.
• The soft cells then smoothly deform into tiles and work in both two and three dimensions.

A team of researchers revealed how theoretical mathematical concepts take on a real-world life when discovering a completely new “soft cell” shape that crossed over from mathematical possibility to abundant natural example.

Mathematicians have long enjoyed the study of shapes. Using sharp edges and plenty of points, they’ve dedicated centuries to seeing just how these shapes fit together for infinite tiling ability. But the equations used in mathematical shaping, with their hard lines and sharp points, don’t generally lead to a lot of crossover with nature.

A team of researchers from Budapest University of Technology recently announced that they have uncovered a new natural class of shape that tiles with curved edges. They uploaded their findings to the preprint server arXiv. Dubbed both “soft cells” and “z-cells,” these shapes lack the telltale corners of theoretical math, but still fit together in both two dimensions and three dimensions.

“A central problem of geometry is the tiling of space with simple structures,” the authors wrote. “The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedral in three-dimensional space are built with sharp corners and flat faces. However, many tilings in nature are characterized by shapes with curved edges, non-flat faces, and few, if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes.”

The team believes that they’ve solved the problem of dimensions with this new “infinite class of polyhedral tilings” that can smoothly deform into soft tiles and construct soft versions of cells generally associated with point lattices in both two and three dimensions.

“These shapes emerge in art, but also in biology,” study lead Gabor Domokos, told the New Scientist. “If you look at sections of muscle tissue, you’ll see the cells having just two sharp corners, which is one less than the triangle—it is a very special kind of tiling.”

“Remarkably, these ideal soft shapes, born out of geometry, are found abundantly in nature, from cells to shells,” the team wrote.

In two dimensions, these soft shell shapes are pretty easy to describe—according to the paper, they are “cells with curved boundaries which have only two corners.” In the three-dimensional space, things get a little more complicated, but the goal is the same: let things be bendy and minimize the amount of “corners” present. In 3D, a soft cell shape can have no corners at all.

“We found that architects have found these kinds of shapes intuitively when they wanted to avoid corners,” Domokos said.

A central part of the paper shows how seashells emerge as a natural example of the shape. Known to form from multiple chambers, shell growth appears to follow a regulated pattern. Using a CT scanner, the team found that when they measured the shells in three dimensions, they couldn’t find corners, even though a two-dimensional view of the shell looked different. That led the team to believe that a seashell offers the prime example of the soft cell shape. It also shows how nature is far beyond our current understanding of geometry.

## The 2023 Popular Mechanics Automotive Excellence Awards: EVs

News Related
• ### The best Walmart Cyber Monday deals 2023

Select independently determines what we cover and recommend. When you buy through our links, we may earn a commission. Learn more. Cyber Monday is almost over and retailers are still offering notable discounts across categories, including tech, beauty, home, kitchen, fitness and subscription services. Everything you need to know about ...
See Details: The best Walmart Cyber Monday deals 2023
• ### Jordan Poole took time to showboat and got his shot blocked into the stratosphere

Jordan Poole took time to showboat and got his shot blocked into the stratosphere Jordan Poole is the basketball gift that keeps on giving. Every week he seemingly finds a new way to do something that’s equal parts incredibly dump and utterly hilarious — and there’s no signs of that ...
See Details: Jordan Poole took time to showboat and got his shot blocked into the stratosphere

Pixelated acronym REIT made from cubes, mosaic pattern Real estate investment trusts (REIT) continue to be incredibly difficult to manage these days. While there are some really high dividend yields out there, that doesn’t necessarily mean these are great buys. Today, we’re going to look at some of the more ...
• ### OpenAI’s board might have been dysfunctional–but they made the right choice. Their defeat shows that in the battle between AI profits and ethics, it’s no contest

OpenAI CEO Sam Altman speaks during the OpenAI DevDay event on Nov. 6. The drama around OpenAI, its board, and Sam Altman has been a fascinating story that raises a number of ethical leadership issues. What are the responsibilities that OpenAI’s board, Sam Altman, and Microsoft held during these quickly ...
See Details: OpenAI’s board might have been dysfunctional–but they made the right choice. Their defeat shows that in the battle between AI profits and ethics, it’s no contest
• ### Russia-Ukraine Drone Warfare Rages With Dozens Headed for Moscow, Amid Deadly Winter Storm

Bad weather along the Russia-Ukraine battlefront is not stopping battles between drones. Knewz.com has learned that one day after Russia sent its most intense drone attack on Kyiv since the start of the war, Ukraine retaliated with dozens of drones sent to Moscow. A Ukrainian pilot trains in drone flights. ...
See Details: Russia-Ukraine Drone Warfare Rages With Dozens Headed for Moscow, Amid Deadly Winter Storm
• ### Trump tells appeals court that threats to judge and clerk in NY civil fraud trial do not justify gag order

Donald Trump urged a New York appeals court to continue to pause the gag order against him in his civil fraud trial, saying that threats to the judge and his law clerk do not “justify” limiting the former president’s constitutional right to defend himself. Lawyers for the New York attorney ...
See Details: Trump tells appeals court that threats to judge and clerk in NY civil fraud trial do not justify gag order
• ### Can Anyone Take Paxlovid for Covid? Doctors Explain.

The antiviral drug can protect some groups from getting severely ill with Covid. Here&#8217;s what you should know about it. WHEN YOU HAVE COVID and aren’t feeling well, you may worry about your symptoms getting worse and that you might end up in the hospital. One option that you have ...
See Details: Can Anyone Take Paxlovid for Covid? Doctors Explain.
• ### Google this week will begin deleting inactive accounts. Here's how to save yours.

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: Google this week will begin deleting inactive accounts. Here's how to save yours.
• ### How John Tortorella's Culture Extends from the Philadelphia Flyers to the AHL Phantoms

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: How John Tortorella's Culture Extends from the Philadelphia Flyers to the AHL Phantoms
• ### Tri-Cities' hatcheries report best Coho return in years

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: Tri-Cities' hatcheries report best Coho return in years
• ### Wild release Dean Evason of head coaching duties

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: Wild release Dean Evason of head coaching duties
• ### Air New Zealand’s Cyber Monday Sale Has the 'Lowest Fares of 2023' to Auckland, Sydney, and More

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: Air New Zealand’s Cyber Monday Sale Has the 'Lowest Fares of 2023' to Auckland, Sydney, and More
• ### NDP tells Liberals to sweeten the deal if pharmacare legislation is delayed

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: NDP tells Liberals to sweeten the deal if pharmacare legislation is delayed
• ### '1,000 contacts with a club': Tiger Woods breaks down his typical tournament prep to college kids in fascinating video

. If you’ve got an old Gmail or Google email account that you haven’t been using, you’ll want to log on quickly before it is deleted. Google in December will begin deleting personal email accounts that have been inactive for two years. That also includes any associated content, including Google Workspace ...
See Details: '1,000 contacts with a club': Tiger Woods breaks down his typical tournament prep to college kids in fascinating video

## Jimmy Carter and all living former first ladies to attend Rosalynn Carter’s memorial service

Former President Jimmy Carter is expected to attend the Tuesday memorial service for his late wife, Rosalynn Carter, in Atlanta, his grandson told CNN – a tribute that will also be ... Read more »

## Rob Reiner to Film ‘This Is Spinal Tap' Sequel in February, Says Paul McCartney and Elton John Will Appear

Rob Reiner to Film ‘This Is Spinal Tap’ Sequel in February, Says Paul McCartney and Elton John Will Appear Forty years after making his directorial debut with the 1984 cult ... Read more »

## Best Buy's Biggest Cyber Monday Deals on Samsung TVs, Sony Headphones, and Dyson Vacuums

Plus laptops and more last-minute deals you don’t want to miss People / Jaclyn Mastropasqua We have reached Cyber Monday is officially here, and there are loads of great deals ... Read more »

## The Joffre Lakes surge returns north of Pemberton

The Joffre Lakes surge is back, much to the dismay of Pemberton and Mount Currie locals. Video footage shared with Pique shows a long line of cars illegally parked on ... Read more »

## Activists calling for Gaza ceasefire begin hunger strike outside White House

Photograph: Jim Watson/AFP/Getty Images Leftwing activists including the actor Cynthia Nixon, famous for her role in Sex and the City, have begun a hunger strike outside the White House aimed ... Read more »

## We just got a first look at McDonald's secretive new spinoff restaurant CosMc's

A construction site in Bolingbrook, Illinois, presumed to be the first location of CosMc’s. Scott Fredrickson McDonald’s has been reluctant to share many details about its planned new restaurant concept ... Read more »

## Conor McGregor’s The Black Forge posts more than \$2 million in losses since 2021 opening

Conor McGregor’s The Black Forge posts more than \$2 million in losses since 2021 opening Conor McGregor made around a \$2 million investment when he purchased the Dublin bar he ... Read more »