Geometry to get to grips with

Cover page: FSB 1204

Spotlight on formal excellence

FSB 1001 | 7607

FSB 1003

FSB 1035 | 7631

FSB 1102

The golden section –a law inherent to both Natureand art

FSB 1160

FSB 1183 | 7674

HandleDuos FSB 1203 | 1204FSB 1208 | 1209

Flush pulls FSB 4252 | 4253FSB 4252 0001 | 4253 0001

Security hardwareFSB 7360 | 7361

2

5

8

10

12

14

16

18

2022

2424

26

True innovations arise whenwell-informed recourse is hadto eternal constants – of whichgeometry is one. Selected de-signers and architects havesounded out its present-day potential to arrive at the FSBdoor hardware set out here.The outcome is geometry to getto grips with: elemental bodiesand classic forms in a contem-porary guise.

Geometry to get to grips with

Conceived by:raumdeutungbüro für gestaltungFalk Horn, Bettina Rudhof

Figs. on pages 6+22: © 2009Estate of Oskar Schlemmer,Munich

1

2

Spotlight on formal excellence

The search begun by Pythagorasfor a mathematically determin -able ordering of the world as aharmoniously ordered cosmos(Greek for universe, order) alsoinforms the philosophy espousedby Plato (427–347 BC).

Plato surmised that Nature’spure forms and regular bodiescannot have come to be bychance but that they reflect theplan of a creator. In his works“Philebos” and “Timaeus”, helinks the elements of Naturewith regularly symmetrical bod-ies. As a consequence, Platoassigns the Earth to the cubeand the air to the sphere, com-pares fire with the pyramid, andlinks water to the cone.

Over and over again architectsand designers have striven toinvent the ideal form. For manycenturies they have made useof measuring and ordering sys-tems from antiquity to this end.Which is what this little work is all about. It shows how thecompositional roots of many amodern idea actually lie in thepast.

The ancient philosopherPythagoras of Samos is consid-ered one of the first mathemati-cians in history. He addressedhimself primarily to geometry,which for the Greeks was themost important branch of math-ematics.

In around 500 BC, Pythagorasdiscovered that there are con-spicuous symmetries betweenmany forms and bodies in Na-ture – from the starfish to theraindrop, from the snowflake to the galaxies. He investigatedthe laws underpinning thesephenomena and distilled theminto mathematically determinablenumerical correlations. His fa-mous observation that, in a right-angled triangle, the sum of thesquare on the hypotenuse isequal to the sum of the squareson the other two sides forms thebasis for geometrical designs.

Illustration of the Pythagoras theorem a²+b²=c²

ac

b

3

Pythagoras’s views on naturalsymmetries led Plato to the sur-prising assumption that regularbodies have their origins in theimmaterial heaven of the godsand that they formed the basisfor the creation of the cosmos.Divine ideas can also be per-ceived in the world – albeit mere-ly as shadows – in the dimen-sions of base geometrical bodies.

The more closely such phenom-ena resemble the base geomet-rical bodies, the nearer they are to the heaven of the gods.This is why, for Plato, the pureforms of the sphere, cube, pyra-mid and cone are the essential-ly beautiful forms and as suchare also true and good.

In his 13-volume work “Ele-ments” published in around300 BC, the ancient Greek math-ematician Euclid drew on Platoto prove that there are five reg-ularly symmetrical bodies:

1. the regular tetrahedron, with four triangular sides(pyramid)

2. the regular hexahedron, with six square sides (cube)

3. the regular octahedron, with eight triangular sides(3-dimensional rhombus)

4. the regular dodecahedron,with twelve pentagonal faces

5. the regular icosahedron, with twenty triangular faces

Sphere, cube, pyramid, cone:The true and good forms according to Plato

The five regular Euclidian bodies

4

Some 250 years later, the Romanarchitect and writer Vitruvius re-ferred to Plato and Euclid in de-vising a theory of beauty ground-ed in the concepts of symme-try, proportion and rhythm, andin the process revived the thesisof the mathematical determin -ability of true beauty. In his “TenBooks on Architecture”, he elu-cidates this thesis by means ofa study of the proportions ofthe human body that Leonardoda Vinci sought to capture in afamous drawing in 1490.

It is Vitruvius we have to thankfor the dimensional ratio of the“golden section”, which has remained an essential part ofcreative knowledge to the pres-ent day. The method of findingbeautiful proportions it gaverise to was adopted in the 20thcentury by the Swiss architectLe Corbusier when he devel-oped his Modulor in the 1940s.

The system draws on humanmeasurements and the goldensection. Le Corbusier initiallyset the standard height at 175cm, raising it to 183 cm (six feet)from 1950, and used the re-spective data to develop a se-ries of further geometrical spec-ifications that all relate to oneanother in the proportion of thegolden section.

Study of the proportions of thehuman body after Vitruvius, drawing by Leonardo da Vinci, c. 1490

The Modulor, after Le Corbusier, 1942

5

Architecture has always servedas a central point of culturalmediation whose great esteemderives from its inevitable asso-ciation with stability and order.This quality is rooted in the geo-metrical purity of its formal com-position.

Pure form has always been avision of architects: they havedreamt from time immemorialof developing objects liberatedfrom all transient effect, insta-bility and disorder. Over and overagain the upshot has been build-ings with straightforward geo-metrical forms: be they cubes,cylinders, spheres, cones, pyra-mids etc., they are fitted togeth-er observing the rules of com-position and hence to the avoid-ance of all conflict.

No form is allowed to disruptanother; at the same time, eachform contributes to the harmo-nious whole. In this way thecomposed geometrical structurebecomes the building’s engineer-ing structure. Form’s purity guar-antees its structural strength.

Things that act on a large scalecan also be depicted on a small-er one: our attempt in this bro -chure to put a series of hard-ware together that embodies therules of past masters, whilst al-so pursuing contemporary de-sign trends, can assist in put-ting the ideal holistic blueprintto effect.

Draft for a high-rise city, Ludwig Hilberseimer, 1924

6

Figurine, after Oskar Schlemmer, 1924

7

Aluminium 1001 | 7607

Its square cross-section lendsthe FSB 1001 model its charac-teristic gripping volume, onethat notably sets off large-formatdoors to advantage. Designedby the architect Peter Bastian,the handle likewise looks greatas a “return-to-the-door” modelfor emergency-exit doors.

Design: Peter Bastian www.fsb.de/1001www.fsb.de/7607

House of Arthur W. Milam, Ponte Vedra Beach in FloridaPerspectival view of the facade, Indian ink on card, Paul Rudolph, 1962Collection of the Museum of Modern Art, New York

9

AluminiumAluGreyStainless Steel

1003

Door handle FSB 1003, whichhas echoes of a miniature dooron its side, is decidedly some-thing of a collector’s item. Johannes Potente adopted theunderlying visual concept andput it to effect in aluminium andstainless steel. We have sinceadded a version in AluGrey®

that sports a striking silvery-greyfinish.

Design: Johannes Potente www.fsb.de/1003

10

Plan of Carolingian monasteryat St. Gall, c. 820 AD, St. Gall Monastic Library

11

Aluminium AluGreyStainless Steel

1035 | 7631

In the autumn of 1996, Düssel-dorf-based interior designerHeike Falkenberg asked FSB torecreate an old handle designfor a renovation job. Using thesketch she submitted, FSB’sDevelopment unit cut a demon-stration model out of the FSB1076 handle. The prototypelooked so good that, togetherwith the designer, we sponta-neously decided to market ourgripping idea. The design wasrapturously received. The ovalcross-section of the grip on FSB1035 is effectively a squashedcircle. This is what produces thefurniture’s characteristic con-tours, which are made up of twosquares and two semicircularplanes.

Design: Heike Falkenberg www.fsb.de/1035www.fsb.de/7631

Model of the solar system after Johannes Kepler, 1596

12

13

Aluminium AluGreyStainless SteelBrass*Bronze

1102

The FSB 1102 model is rootedin a redesign venture by Italiandesigner Alessandro Mendini,who refashioned the celebratedGropius lever handle by using a different material and addinga groove as one of his submis-sions to FSB’s Design Workshopheld in 1986. We now supplyFSB 1102 in the five materialslisted above and the correspon-ding finishes. We would recom-mend using the rugged stain-less steel variant on heavily useddoors.

* only rose versions and back-plates 1418 .. and 1451 ..(standard bearing)

Design: Alessandro Mendini www.fsb.de/1102

14

The golden section –a law inherent to both Nature and art

Though initially amenable torepresentation in geometricalforms, it is also to be found innatural phenomena. A ratio of5:8 has been established in theleaves of many plants, for in-stance. From a sample of 500oak leaves, 235 exactly corre-spond to the proportions of thegolden section, 93 differ by 1mm and 92 display deviationsof 2 mm. In addition to suchreadily perceivable instances ofconcurrence, Nature also con-tains complex structures suchas the growth spiral. Mathemati-cians call this phenomenon ofregular formal curvature ‘dilata-tion’.

The term is used to describe aform that twists to mathemati-cally definable structures andshrinks at the same time. Dilata-tions are to be found in snailshells just as they are in pinecones. They taper to a pointwhilst simultaneously spirallingaround.

The golden section defines adimensional ratio in the first in-stance. The sectioning involvedis merely figurative, the purposebeing to harmoniously relate twodiffering parts of a line to oneanother. A line is divided intotwo unequal segments in sucha manner that the smaller is inthe same ratio to the larger asthe larger is to the line as awhole. The golden section canbe expressed in terms of themathematical equation a:b=b:(a+b). Applied to a numeri-cal series, this gives rise to aconstant sequence in which thelast two numbers are added to-gether: 1, 1, 2, 3, 5, 8, 13, 21,34, 55, 89, 144 ... Disregard -ing the first four cases, dividingany number in the series by theone that follows always roughlyyields the value 0.618; similarly,division by the preceding num-ber yields 1.618 or thereabouts.

These two numbers determinethe ratio between the segmentsof the golden section. The “ma-jor” segment of any line is 1.6times larger than the “minor”,which is accordingly arrived atby dividing the known length ofthe former by 1.6. The goldensection proves to be of reliableassistance in arriving at beauti-ful proportions when applied tothe size ratios within any two-dimensional structure.

The section through a nautilusshell renders the growth spiral visible.

15

Phenomena of this kind are referred to in mathematics as“logarithmic spirals”. Close in-spection of a buttercup revealsthat the yellow petals form astructure made up of juxtaposedlogarithmic spirals. The factorby which the spirals increase in size is exactly 0.6181. It’s asthough Nature were bent onapproximating as precisely aspossible to the ideal mathemat-ical base form, since the pro-portionality of this natural spiralclearly squares with the goldensection. The same applies tothe sunflower, whose seeds arearranged in right and left-hand-ed spirals. The plotted diagramillustrates the link with the abovenumerical series of 1, 1, 2, 3,5, 8, 13, 21 etc.

Beautiful dimensional ratio asformal precept for utilitarianobjects

All such studies and age-old in-sights are factored into the de-sign of utilitarian objects. Thusit was that the dynamic form ofthe growth spiral served as theformal role model for a series of door handles: echoing the dilational curve, handles in theFSB 1160 series curve stylishlyround from neck to tip, becom-ing ever thinner in the process –just as much a treat for the eyeas for the hand.

Regularity of the growth spiralestablished by mathematical means

16

Logo of the “Theory of Archi -tecture” Department at BTUCottbus

17

AluminiumAluGrey Stainless Steel

1160

Works design FSB 1160 recre-ates the “dynamic golden growthspiral” (cf. p. 15) in the form of a round cross-section, withthe lever handle likewise taper-ing from the neck to the end ofthe handle in conformance with the rules of the golden section.This narrowing heightens themomentum of the natural curve.The design is restrained, goodto hold and features direction-of-motion styling.

www.fsb.de/1160

Perspectival study sheet with countryside scenery, Friedrich Gilly, 1799

19

Aluminium Stainless Steel1183 | 7674

Hadi Teherani breaks with tra-ditional thinking in FSB 1183.We are all familiar with the“Wittgenstein solution” for nar-row-frame doors in which astandard lever handle is pairedwith a contrasting – cranked –design on the slamming face.Hadi Teherani has radically reduced the diversity of such handle models: he delivers thefunction of the cranked leverhandle model – averting thedanger of fingers getting caughtin the slamming area of framedoors – by shifting the handle’spoint of rotation leftwards. HadiTeherani’s emergency exit mod-el boasts a similarly radical re-turn to the door: he simply takesa third of the grip section andattaches it to same at right an-gles.

Design: Hadi Teherani www.fsb.de/1183www.fsb.de/7674

20

Stainless SteelHandleDuo 1203 | 1204

A modern, clean-lined formalvocabulary is the trademark ofBerlin architects Ivan Reimannand Gesine Weinmiller. Theychampion elemental forms andlove reduction. The handle duothey have come up with encap-sulates this approach: two an-gular bodies in stainless steelhaving elemental geometricalforms give rise to a three-dimen-sional pattern whose severe el-egance derives from the visualinterplay of trapeze and rectan-gle and of line and plane. Theshort neck of one handle pro-trudes from the door as an up-right rectangle, that of the otheras a flat rectangle. There is thesame perceptual interplay whenthe grip sections are viewedfront-on. While one model pres-ents itself to the observer flat-on to highlight the trapezoidal styling of its neck, its counterpart

PROUNInterpenetrating Planes, after El Lissitzky, 1920

is a horizontal block that hasseemingly undergone planarelongation. Backplates cut fromsolid material reinforce the em-blematic effect of these elemen-tal bodies.

21

Design: Ivan Reimann,Gesine Weinmiller

www.fsb.de/duos

22

Stainless SteelMacassar Grip HandleDuo

1208 | 1209

Stuttgart architect duo Stefanieand Martin Naumann set abouttheir remit in a soberly pragmat-ic vein: “Resisting the urge tobe showy, we have opted for avery straightforward path after along, hard tussle. We have ad-mittedly risked treading whereothers have trodden before, butthere’s not necessarily anythingwrong in that.” There’s certainlynothing wrong with their handleduo, whose archaic simplicityand purist linearity could besaid to constitute the base mod-el for all handle duos. Formingthe point of departure are thevarying sequences of movementsinvolved in operating doors:“Doors have two sides and eachis different. One side comes atyou whilst you have to shovethe other one away, on one side you have to use your ownhand as a brake to avoid being

Geometrical Man, after Oskar Schlemmer, 1924

squashed against the door re-veal whilst on the other youhave to firmly take hold.” Thedesigner duo have drawn thefollowing formal consequencesfrom these push/pull constraints:both handles have the samebasic form but can be told apartby design details indicative ofthe different ways in which han-dles are taken hold of. The han-dle with which a door is pushedopen features a clearly visible“thumb rest”, whilst the handleused to pull a door open hasbeen given a “forefinger furrow” – all very much in line with ourFour-Point Guide to Good Grip(-pability).

23

Design: Stefanie and Martin Naumann

www.fsb.de/duos

24

Aluminium Stainless Steel

FSB delivers a formally and func-tionally innovative hardware so-lution for sliding doors in theform of either enclosed or openflush pulls. These echo in exem-plary fashion the architecturaltrend towards the flush-mount-ing of functional appliances.Enclosed flush pulls ensure auniform appearance for the doorleaf. The operating aperture isalways blanked out by a flap thatsprings neatly into the closedposition when the hardware isnot being used.

Study of the proportions of the human body after Vitruvius, drawing by Leonardo da Vinci, c. 1490

Flush pulls

25

42524252 0001

42534253 0001

www.fsb.de/flushpulls

Security hardware

26

Stainless Steel

Adopting a radically purist approach to design, FSB’s in-house designer Hartmut Weiseintroduces a security hardwaredesign with FSB 7360 and FSB7361 that departs radicallyfrom received formal concepts:using stainless steel 5 mm thickhe has created a matter-of-factsculpture of folded surfaces that makes no concessionswhatsoever to its intended door.The design is only availablewith an S4 security rating and,besides a classic version, op-tionally comes with an integrat-ed electronics package in theform of a capacitive door-bellsensor plus nameplate and radio-operated door-bell module anda harmonised radio gong on theinside.

House III, axonometric representation, Peter Eisenman, 1970

FSB supplies both models asentrance door furniture with asecurity-coordinated straight-cornered backplate and an FSB1108 lever handle on the inside,Security Class S4 - ZA (cylinderprojection 8 –16 mm), with 92mm lock centres and a 10 mmspindle hole.

www.fsb.de/7360www.fsb.de/73617360 7361

28

Church of San Carlo alle Quattro Fontane, Rome, representation of the geo -metrical ground plan, afterFrancesco Borromini, 1634

“Geometry is important not solely on account of its practical merits but because it investigates objects that are eternal and unchangeable and strives to raise the soul to truth.“ Plato, 360 BC

Franz Schneider Brakel GmbH + Co KG

Nieheimer Straße 38 33034 Brakel Germany

Phone +49 5272 608-0 Fax +49 5272 608-300 www.fsb.de · info@fsb.de 0

0498

022

3 90

01 ·

06

|201

0