IT’S inexplicable: people seem to like some rectangles more than others. Present them with a range of choices, from fat and square to long and thin, and they will pick out as most “pleasing” the rectangle with side lengths closest to a particular ratio.
This number – known as the golden ratio, or phi – has been celebrated as a fundamental of aesthetics and is believed to have been used all over the place, from Greek architecture to the framing of the Mona Lisa’s face. But phi crops up in the sciences too. And its latest appearance, in the properties of some particularly weird metals, has recently been published in Physical Review B, a journal of solid-state physics not noted for its contribution to art history.
Indeed, the art world has long been losing its traditional grip on phi. We now know that the golden ratio crops up in the arrangement of leaves on plant stems, the shape of a sunflower’s seed head and a seashell’s spiral, and even the properties of spinning black holes. It’s simply everywhere in our Universe. What we don’t know is why.
The golden ratio was first described explicitly by the Greek mathematician Euclid of Alexandria around 300 BC, although it was probably known to the followers of Pythagoras two centuries earlier. Euclid defined it in terms of a line divided into two unequal segments (see Graphic). The ratio of the longer segment to the smaller one is said to be in the golden proportion if it is equal to the ratio of the whole line to the longer segment. Numerically, the golden ratio is equal…
![Astronomers have long known that understanding how star clusters come to be is key to unlocking other secrets of galactic evolution. Stars form in clusters, created when clouds of gas collapse under gravity. As more and more stars are born in a collapsing cloud, strong stellar winds, harsh ultraviolet radiation and the supernova explosions of massive stars eventually disperse the cloud, and their light can bear down on other star-forming regions in the galaxy. This process is called stellar feedback, and it means that most of the gas in a galaxy never gets used for star formation. Researching how star clusters develop can answer questions about star formation at a galactic scale. Now, the state of the art has been further developed with both Hubble and Webb working together to provide a broad-spectrum view of thousands of young star clusters. An international team of astronomers has pored over images of four nearby galaxies from the FEAST observing programme (#1783), trying to solve this mystery. Their results show that it is the most massive star clusters that clear away their gaseous shroud the fastest, and begin lighting their galaxy the earliest. The team identified nearly 9000 star clusters in the four galaxies in different evolutionary stages: young clusters just starting to emerge from their natal clouds of gas, clusters that had partially dispersed the gas (both from Webb images), and fully unobstructed clusters visible in optical light (found in Hubble images). With Webb???s ability to peer inside the gas clouds, they were able to then estimate the mass and age of each cluster from its light spectrum. This image shows a section of one of the spiral arms of Messier 51 (M51), one of the four galaxies studied in this work, as seen by Webb???s Near-Infrared Camera (NIRCam). The thick clumps of star-forming gas are shown here in red and orange, representing infrared light emitted by ionised gas, dust grains, and complex molecules such as polycyclic aromatic hydrocarbons (PAHs). Within these gas complexes, each tens or hundreds of light years across, Webb reveals the dense, extremely bright clusters of massive stars that have just recently formed. The countless stars strewn across the arm of the galaxy, many of which would be invisible to our eyes behind layers of dust, are also laid bare in infrared light. [Image description: A large, long portion of one of the spiral arms in galaxy M51. Red-orange, clumpy filaments of gas and dust that stretch in a chain from left to right comprise the arm. Shining cyan bubbles light up parts of the gas clouds from within, and gaps expose bright star clusters in these bubbles as glowing white dots. The whole image is dotted with small stars. A faint blue glow around the arm colours the otherwise dark background.]](https://images.newscientist.com/wp-content/uploads/2026/05/13114322/SEI_296271016.jpg)
