It moves us, delights us – draws us, spellbound, towards it. Since antiquity, humans have been searching for the secret of beauty. It comes down to mathematics – and fractions.
Beauty fades? No. Beauty endures! Fashions may come and go. Sometimes skirts are short, sometimes beards are long. Sometimes cars crouch like predators; sometimes they look like fortresses on wheels. However, the basic shapes behind them, the faces and patterns which appeal to us, remain the same, as they follow an age-old constant which is so ancient that it could effectively be seen as a universal standard. Five to eight, that is the formula – a simple measure of proportion, which is also called the golden ratio. If you divide a length using these proportions, the split lies within the golden ratio. Anything that conforms to these proportions, in form and composition, has an immediate attraction for us humans. If you show someone a group of rectangles, they will prefer the one whose sides have a length ratio of five to eight; photographers always position the main elements of their pictures away from the center; paintings by old masters, Greek temples, the pyramids of Gizeh and the Apple logo are all constructed in this way.
Since antiquity, humans have been tracing the power of proportion. First came the mathematicians: Euclid documented it for the first time 300 years before Christ. Then came artists and designers, who worked and experimented with it. Plants, animals, human bodies: they all harbor this five-to-eight ratio within them. In horses, the foreleg marks the golden ratio, in bees it is the narrow place between thorax and abdomen, in humans it is the navel. Leonardo da Vinci drew the golden ratio on the Vitruvian Man, whose proportions still count as the universal beauty ideal. Today, we know that it was this physique that, long ago, enabled us to walk. Long legs give us energy-saving leverage and allow us to travel long distances at high speed. Walking upright makes us human.
And yet – there is a formula that lies even deeper than the golden ratio. In the year 1202, Italian mathematician Leonardo Fibonacci noted a sequence of numbers that follow a particular logic. The sum of the two previous numbers always gives the next one: 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. If you divide a number by the next lowest, the result comes closer to a rounded 1.6180, the higher you go – just like when you divide eight by five. Just a gimmick? Absolutely not. Walk through a garden sometime. You will see buttercups with five petals, larkspurs with eight, marigolds with 13, asters with 21. The leaves are always arranged at the golden angle of 137.5 degrees, a growth pattern that follows the golden ratio. This arrangement ensures that no leaf obscures another and each one receives as much light as possible. The scales of pineapple fruit, romanesco and pine cones are arranged in a spiral pattern, as are the kernels of sunflowers. The number of left and right curving spirals in a fruit corresponds to two consecutive Fibonacci numbers – and of course, they also curve at the golden angle. Just like nautilus shells, snail shells, cyclones and spiral galaxies.
Proportions create strength. Angles unleash momentum, regulating principles that ensure nourishment is available to all; the universe bears life according to a pattern. As we have always existed within this universe, we recognize it intuitively, feel safe and secure within it. Every encounter with this pattern is a primeval moment, bringing joy. Regardless of background and experience, all humans light up when they see, hear or feel something beautiful. Neurologists have located the area of the brain that perceives beauty: it is in the frontal lobe of the cerebrum, just behind the eyes, and is one of the areas that are always active when we are making decisions.
Coppi Barbieri / Trunk Archive
Organic curves: as the light plays, the shape begins to dance. This is true of both the calla lily and the Heydar Aliyey Center, a building designed by architect Zaha Hadid in Baku, Azerbaijan
Haussmann. Design: Trix & Robert Haussmann.
Georges Dambier, Capucine in hat by Jean Barthet, Arachnée, April, 1952
The allure of regularity: patterns create depth and catch the eye. The Haussmann 310 chair by Walter Knoll , and the actress Capucine wearing a Barthet hat in 1952
Tama Desk. Design: EOOS.
oxygen / Getty Image
The poetry of momentum: the natural-looking lines of the Walter Knoll Tama Desk and the cloud of silk on the right were formed with a flick of the wrist
This means: beauty is never merely beautiful. Beauty helps our perception. It helps us to master life, to reduce complexity. Beauty makes sense. Something beautiful creates trust, it signals truth, goodness and kindness: even as babies, we look at beautiful faces for longer. And so, in human creations – in paintings, design, houses and fashion – we also celebrate the eternal aesthetic formula. Le Corbusier used the golden ratio and the dimensions of the human body for his modulor, a system of proportions for furniture and buildings on a human scale. Then there is Max Bill, Bauhaus scholar, architect and designer: his minimalistic clock designs are still effective today. His graphic prints, which play with loops, spirals and patterns, also have a timeless beauty. An aesthetic based on mathematical principles – this was Max Bill’s great theme.
And yet – however secure we feel in the mathematics of beauty – we need small aberrations. All life also shows itself to be continually chaotic, wild, full of anomalies. Perfectly symmetrical faces are irritating, appear inauthentic and inspire mistrust. Small flaws need to be there, to lend personality – only then do we see someone as truly beautiful. Madonna’s tooth gap, Marilyn Monroe’s beauty spot, inclusions in a gemstone – the highest ideal is found in the balance between regularity and coincidence. Nature always perfects the relationship between these two forces.
Perfect imperfection – this also applies to Walter Knoll. For example, each marble slab of Oki Table and Joco Stone tells its own petrified version of the history of Earth. The brass-surfaced tables are also unique pieces, as the metal shows the finest traces of the polishers who gave it its last finish. This is what gives Walter Knoll products their allure – the allure of their beauty.
mauritius images / Chris Wildblood / Alam
Misty Copeland, principal American Ballet Theatre, photographed by © Henry Leutwyler
Balancing act: lightness grows from firm foundations, the greatest art from the most delicate work. Termite mounds in the north of Namibia, and the foot of a ballerina dancing en pointe
Oota. Design: EOOS.
Emma Backer / Shutterstock
Bold composition: meshwork meets smooth surfaces, straight meets diagonal. The tension here is created by the rotation of the lines. Oota Table by Walter Knoll , and the Fulton Center in New York City
Playing with alluring forms like this begins early in the design phase. Walter Knoll creates products with lines that are, in fact, rational. And yet, to these rational lines Walter Knoll adds a creative twist, as in Oota Table. Its delicate wickerwork plays with graphic rhythms that draw an emotional response.
We love perfection, if it lives and breathes. As our materials – wood, fabrics, leather – are natural, they embrace change. They mature. Just think of the patina that our saddle leather gains over time. We stroke our fingers over well-used surfaces, over small flaws and scars. Over the grain of a piece of wood, in order to feel the history of its growth. Beauty is what is revealed when we master the creative process. Its matrix is what allows the energy of life to flow. And so, beauty gives us humans fresh nourishment every day. It explains the present, gives us a future – promises eternity.
Text: Hiltrud Bontrup