A comparative analysis on the theme of geometry

A C O M P A R AT I V E A N A LY S I S ON T H E T H E M E O F G E O M E T RY

Altes Museum – Neue Nationalgalerie Karl Friedrich Schinkel – Mies van der Rohe

Heijkoop,V. (Vivianne)

Karl Friedrich Schinkel Altes Museum

4

Mies van der Rohe Neue Nationalgalerie

5

INDEX

INDEX E S S AY A N A LY S I S

7 9

3.1.1 Dimensions

12

3.1.2 Dimensions - proportions colonnade

16

3.1.3 Dimensions - position of columns

18

3.2 Columns - classical proportions

19

3.3.1 Composition of the facade - repetition

20

3.3.2 Composition of the facade - variation

22

3.3.3 Composition of the facade - rhythm

24

3.3.4 Composition of the facade - symmetry

26

3.3.5 Composition of the facade - hierarchy

30

3.3.6 Composition of the facade - similar proportions

32

3.4.1 Order or spaces - repetition and variation

34

3.4.2 Order or spaces - rhythm

36

3.4.3 Order or spaces - symmetry

38

3.5 Geometry

42

7

8

E S S AY

Rules as guidance, not as principle

“Architecture is composition”. (Ungers, 1964) This is

Schinkel’s Altes Museum”. (Durth & Roland, 2007) Yet, in

the message of the inaugural lecture of O. M. Un-

their appearance they are not convincingly similar.

gers. In architecture many disciplines and elements

At first sight they appear rather different in their

are brought together, that need to fit in one con-

expression and shape.

stituent whole. Bringing together these elements

The Altes Museum presents itself as a harmonious

and disciplines isn’t always an easy task. It demands

whole, as it finds through lineamenta “its inner rest

creativity and practice to come to a satisfying com-

in the worthy form and order” (Apelt, 2016) (Analysis 3.5).

position. A guidance to achieve this, as argued by

It is designed from a system of walls, consequent-

Ungers, is “to construct a framework of rules.”. (Un-

ly giving a repetition of floorplans at the different

gers, 1964) When a set of rules is taken as the design

levels. (Analysis 3.4.1) The dimensions of the volume

principle, relations are defined and repeated that

relate to each other, for the building is based on

will lead to harmony in the design. (Thiersch, 1883)

returning measures.The dimensions of the Rotun-

These rules could be taken as either an absolute

da are similar in height and width, and return in

criteria or taken by own interpretation. However,

the width and length of the floor plan. (Analysis 3.5)

Durand warns us for disposition: “Only when it is

The visible element of the Neue Nationalgallerie

fitting and it is economical, it will become the source

for the city is the volume that shapes the top floor,

of the pleasurable sensation that buildings convey to

placed on a large podium. The podium hides the

us.”. (Durand, 1802)

irregularity of the floor underneath. The design is based on a grid of columns that creates a free

Anyhow, who thinks that a strict set of rules is

floorplan to provide flexibility. The top volume

tedious and will lead to similar and reproducible architecture is wrong. Proof can be given by

presents itself firmly, though friendly as a floating

a comparison of the Altes Museum by Karl Frie-

slab on a transparent volume. It appears very clear

drich Schinkel and Neue Nationalgallerie by Mies

in all section, elevation and plan. (Analysis 3.5) The

van der Rohe.

roof slab is hierarchical and absorbs the attention from the volume. It is a geometry of clear bound-

These two buildings have been compared often

aries and rectangular shapes.

in architectural theory. The Neue Nationalgallerie

Both architects tackle the measures of their build-

by some is “interpreted as the modern equivalent of

ing from another perspective. Whereas

9

Schinkel describes the dimensions

van der Rohe”, 2016) Anyway, the Altes Mu-

from the visitor’s point of view1, Mies

seum and the Neue National Gallerie

describes the dimensions from a grid.

are both an analogy to the Greek Tem-

(Analysis 3.1.1) Nevertheless, in

ples of the Ionic order.

both sym-

metry structures the plan and hierarchy

Comparable to the Greek Temples, the

is given to the upper floor. (Analysis 3.4.3

buildings introduce themselves by a col-

) (Analysis 3.1.1)

onnade, an outside space that diverts from the buildings volume by an array

However, the careful eye will notice

of columns. This colonnade, though in

that these building are closer togeth-

the Neue National Gallerie present all

er than expected from its geometry.

around the building but by just two col-

When studying the dimensions, it is

umns and in Altes Museum only present

noticed that both buildings derive from

in the front façade but by 18 columns, in

the classical proportions of the ionic

plan appear in a ratio of 1 in 7. (Analysis

order. (Analysis 3.2) Schinkel treated this

3.1.2)

1 – “Eventuelly, I developed the following design for the building. It has a rectangular form of 276 feet 3 inches in length and 170 feet 4 inches in width.There are two interior courtyards, 57 feet long anf 52 feet 6 inches wide. Minus those two courtyards, there will be a floor area of 41,083 square feet.The height of the building up to the cornice is 61 feet. Of this dimension the lower story accounts for 5 feet 5 inches, the first story accounts for 20 feet 7 inches, and the second story accounts for 28 feet 3,5 inches. “ (Butterworth Architecture, 1989)

very strict in the composition, as every dimension relates to the Ionic order.

Now that this new knowledge is gained,

Though, not as prominent as in Altes

another look can be given to the ap-

Museum, similar proportions are to

pearance of the buildings, in a study of

be found in the Neue Nationalgallerie.

the façade. Both facades consist of a

Strongly abstracted the proportions of

repetition of elements. The repetition

2

the three main parts of the order – “a

of elements creates rhythm. (Analysis

pedestal, a column and an entablature”

3.3.1) (Analysis 3.3.3)

In the Altes muse-

– remain. Seen from the

um it is created through the elements

plinth on, the column height and the

themselves, as in the Neue Nationalgal-

thickness of the roof slab proportion-

lerie it is put forward through its de-

ally relate to the columns diameter ac-

tailing, by the strongly present lines in

cording to the Ionic order.

the building elements. Both facades are

These proportions are the ‘framework

clear and readable, through the repeti-

of rules’ for the Greek Temples of the

tion of recognizable elements. They de-

Ionic order. The Neoclassical architec-

scribe a meaningful pattern, and grant

ture has re-interpreted these propor-

hierarchy.

tions in their designs, and now Mies has

The facades solve a mystery in the plans

brought them back in what could be

of the Neue National gallery. From the

called modern classicism. (“Ludwig Mies

plan it appears that the dominant col-

(Durand, 1802)

10

2 - “Just as, in general, an order comprises three parts, a pedestal, a column, and an entablature; and as we then distinguish within the pedestal a plinth, a dado, and a cornice; within the column a base, a shaft, and a capital; and within the entablature an architrave, a frieze, and a cornice: similarly, each one of these parts in its turn includes several others, which are themselves composed of other, even smaller parts” (Durand, 1802)

umns deviate from the strongly visible grid. (Analysis 3.1.3) As

Mies is often described as an architect of

- Apelt, H. (2016, 05 11). Lecture 3 Geometry.

the grid, this looks like a contradiction in his own design strategy. However, there’s good reason for

- Bohnstedt, L., Bühlmann, J., Durm, J., Thiersch, A.,

it. The study to the facade opens up a new dis-

& Wagner, H. (1883). Die architektonische Compo-si-

covery on the proportions. The facades of both

tion: Allgemeine Grundzüge die Proportionen in der

buildings can roughly be divided in three faces. To

Architektur die Anlage des Gebäudes; die Gestaltung

achieve harmony, Mies van der Rohe placed the

der äußeren und der inneren Architektur; Vorräume,

columns at such so that the outer faces of the

Treppen-, Hof- und Saal-Anlagen. Darmstadt: Diehl.

façade achieve similar proportions as the outer faces of the façade of the Altes Museum. (Analysis

- Butterworth Architecture (1989) K.F. Schinkel

3.3.7)

Sammlung Architektonischer Entwurfe, Princeton Ar-

According to Adolf Thiersch “The harmonious

chitectural Press.

emerges only through the repetition of the main figure in all the parts of the work.”. (Thiersch, 1883) When

- Durand, J. N. (1802). Précis of the Lectures on Archi-

reflecting this on the Neue Nationalgallerie, the

tecture. Section Three. Forms and Proportions.

repetition of elements, the rhythm and following rules of proportions result in a harmonious com-

- Durth, W., Roland, M. (2007); ‘Schinkel’s Order, ra-

position.

tionalist Tendencies in German Architecture’.

Ultimately it is evident that both buildings are

- Ludwig Mies van der Rohe. (2016, 06 27). Opge-

clear an readable buildings. The designs derive

haald van Kunstbus: http://www.kunstbus.nl/archi-

from the classical proportion, that in both func-

tectuur/ludwig+mies+van+der+rohe.html

tions as ‘the framework of rules’. However, in the design of the Neue Nationalgallerie the classical

- Ungers, O. M. (1964). What is architecture? In

order gives direction, yet no solution. Mies van

The rationalist reader: Architecture and rationalism in

der Rohe gives his own interpretation to these

Western Europe, 1920-1940/1960-1990 (pp. 318-

rules, and integrates them in a new structural sys-

322). London: Routledge.

tem. By the repetition of elements, the hierarchy given by the entablature and making right use of proportions, both buildings arrive at a harmonious composition.

In the end two great pieces of architecture were found from a same set of rules, yet being very different in their expression and shape.

11

8,8 m

16,0 m

27,7 m

16,0 m

9,1 m

9,1 m

4,9 m

4,9 m

17,4 m 37,6 m

17,4 m 37,6 m

9,1 m

9,1 m

6,4 m

6,4 m

8,8 m

8,8 m

84,2 m

16,0 m

27,7 m

16,0 m

8,8 m

84,2 m

Ground oor - 1:2000

3.1.1 Dimensions

The dimensions describe the key measurements of the building, as designed the architect.

According to his own notes, Schinkel describes his design from what the eye sees, what the visitor receives as information when looking at the design. (Butterworth Architecture, 1989) Therefor, the measurements of Dimensions

the design are analysed from the visitors perspective/from within. Some dimensions are repeated due to the symmetrical layout of the plan.

Butterworth Architecture (1989) K.F. Schinkel Sammlung Architektonischer Entwurfe, Princeton Architectural Press.

12

64,8 m

64,8 m

A

64,8 m

B

64,8 m

A

64,8 m

64,8 m

Upper floor - 1:2000

A

64,8 m

B

Basement - 1:2000

3.1.1 Dimensions

The architecture of Mies van der Rohe is based on a grid. (Vandenberg, Dimensions outline Grid Reflection first floor

1998) In the Neue Nationalgalerie, the grid measures 7,2 m. All dimensions relate to this grid. The glass facade is set 7,2 m to the back compared to the roof., whereas the basement is a multiple of 14 by 15 times the basic grid measure.

Vandenberg, M. (1998). New National Gallery, Berlin. London: Phaidon Press Ltd.

13

6,7 m

6,7 m

8,6 m

8,6 m

6,3 m

6,3 m

1,65 m 8,8 m

27,7 m

16,0 m

16,0 m

1,65 m

8,8 m

8,8 m

16,0 m

84,2 m

27,7 m

16,0 m

8,8 m

84,2 m

Section A - 1:2000

6,4 m

9,1 m

23,3 m

8,6 m

8,6 m

6,3 m

6,3 m

1,65 m

1,65 m

9,1 m

6,4 m

9,1 m

23,3 m

9,1 m

Section B - 1:2000

6,7 m

6,7 m

12 m18,6 m

12 m 18,6 m

4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m

4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m 4,25 m

84,2 m

84,2 m

South elevation - 1:2000

3.1.1 Dimensions

In section the building can be divided into three floor,s each with a different ceiling height.The upper floor is the highest floor, making it hierarchical over the lower floor.

Strongly present dimensions Other present dimensions

In elevation the building van be divided into three horizontal segments, a plinth, a base and an entablure. The columns of the front elevation are repeated every 4,25 m center to center distance.

The measurements do not relate to each other according to a grid.

14

7,2 m

28,8 m

2,0 m

2,0 m

8,0 m

8,0 m

7,2 m

18,0 m

28,8 m

18,0 m

64,8 m

64,8 m

Southeast elevation - 1:2000

Section A - 1:2000

Section B - 1:2000

3.1.1 Dimensions

In section the building can be divided in two floor, of which the upper floor has a high ceiling height “five times the height of a man” (Vandenberg, 1998) making it hierarchical over the lower floor.

In both section and elevation the grid gives direction for the measures Dimensions outline Grid

of the building. All building elements are placed at a multiple of the basic grid size.

Vandenberg, M. (1998). New National Gallery, Berlin. London: Phaidon Press Ltd.

15

7

7

1

1

Ground oor - 1:2000

3.1.2 Dimensions - proportions colonnade

The measurements of the depth of the colonnade compared to the depth Dimensions

of the rest of the builin volume is according to a ratio of 1:7.

16

A

7

7

1

1

B

Ground oor - 1:2000

3.1.2 Dimensions - proportions colonnade

The measurements of the depth of the colonnade compared to the depth of the rest of the building’s volume is according to a ratio of 1:7. Though, the colonnade in the design of the Neue Nationalgallerie is not determiDimensions Grid

nally present as it only consists of two columns along each facade. This is due to the economic and industrial system of the building.

17

A

B

Ground oor - 1:2000

3.1.3 Dimensions - position of columns

The design of the Neue Nationalgallerie is based on a grid, yet one of the most dominant building elements deviate from the grid. The eight large Dimensions Grid

columns that carry the load of the roofslab are positioned in between gridline. Seen from the perspective of the grid, this seems dispositioned.

18

2 1/4 d

2 1/4 d

5/6 d

9d

9d

9/10 d

d = 0,95 m

d = 1,3 m

Section of facade - 1:200

Section of facade - 1:200

3.2 Columns - classical proportions

The classical order deďŹ nes proportions and relationships of forms and dimensions of building elements in the design.

With the diamter of the column taken as a base unit, it is analysed how the measurements of other building parts relate to the diameter.

In both buildings the diameter proportionally returns in the design, according to the Ionic order.Though in the Neue Nationalgallerie its details Dimensions

are strongly abstracted, in the basic dimensions it is present.

19

South facade - 1:2000

North facade - 1:2000

West facade - 1:2000

3.3.1 Composition of the facade - repetition

Repetition element 1 Repetition element 2 Repetition element 3 Repetition element 4 Repetition element 5

Repetition is the repeated use of elements that is not due to symmetry.

The facade of the Altes Museum is composed from the repetition of elements. The front facade is treated differently as the composition exist sof columns. The side facades are treated equally and are composed by a repetition of windows.

20

Southeast facade 1:2000

Northeast facade 1:2000

3.3.1 Composition of the facade - repetition

Repetition element 1 Repetition element 2 Repetition element 3

The facade of the Neue Nationalgallery is composed from the repetition.

Each facade is equal in appearance, therefor the repeated elements are similar in all facades, excisting of a roof element, a column and a glass panel.

21

South facade - 1:2000

North facade - 1:2000

West facade - 1:2000

3.3.2 Composition of the facade - variation

Variation are the deviating elemtents that appear only once, or twice when due to symmetry.

The variation in the facades of the Altes Museum are at the edges. The Variation element 1 Variation element 2 Variation element 3 Variation element 4

columns at the edges appear in different shape than the other columns, or other parts of the facade. Furthermore, ornaments are placed at the edges to accentuate them. The variation gives the facade a startingpoint and an endpoint. In introduces as well as ďŹ nishes the facade.

22

Southeast facade 1:2000

Northeast facade 1:2000

3.3.2 Composition of the facade - variation

The facades of the Neue Nationalgallery have no variation in them. The top volume and its facades appear the same on all sides. The variation is Variation element 1

found in the square and the basement, who are subject to the top volume.

23

South facade - 1:2000

North facade - 1:2000

West facade - 1:2000

3.3.3 Composition of the facade - rhythm

Rhythm “is movement or procedure with uniform or patterned recurrence of a beat, accent, or the like.”. (Dictionary, 2016) In the Altes Museum the rhythm is caused by the interval of repeting elements. The variation sets a firm note at the beginning and end, introRhythm

ducing and finishing the equal rhythm in the middle.

Rhythm. (2016, 06 27). Retrieved from Dictionary: http://www.dictionary.com/browse/ rhythm

24

Southeast facade 1:2000

Northeast facade 1:2000

3.3.3 Composition of the facade - rhythm

In the Neue Nationalgallerie the rhythm is accentuated by the strong lines in the facades appearance, due to its detailing. The columns magnitude the rhythm and set a ďŹ rm note at the beginning and end, and in Rhythm

between. They proportionally interupt the equal rhythm in the middle.

25

South facade - 1:2000

North facade - 1:2000

West facade - 1:2000

3.3.4 Composition of the facade - symmetry

Symmetry “is the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts.� (Dictionary, 2016) The front and back facade are absolute symmetrical. The side facades First symmetry Second symmetry

contain a shifted symmetry, as the dome is not centrally located in the building, but is set back due to the colonnade of the building.

Symmetry. (2016, 06 27). Retrieved from Dictionary: http://www.dictionary.com/browse/ symmetry?s=t

26

Southeast facade 1:2000

Northeast facade 1:2000

3.3.4 Composition of the facade - symmetry

Symmetry is the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts.

First symmetry

The facades of the Neue Nationalgallerie are absolut symmetrical.

27

South facade - 1:2000

North facade - 1:2000

West facade - 1:2000

3.3.4 Composition of the facade - symmetry

First symmetry Second symmetry Third symmetry Fourth symmetry Fifth symmetry

All building elements have symmetry in themselves..

28

Southeast facade 1:2000

Northeast facade 1:2000

3.3.4 Composition of the facade - symmetry

First symmetry Second symmetry Third symmetry

All building elements have symmetry in themselves..

29

South facade - 1:2000

North facade - 1:2000

West facade - 1:2000

3.3.5 Composition of the facade - hierarchy

Hierarchy are elements that appear more important due to their size, shape or position.

The hierarchic element of the Altes Museum is the cornice of the entablure. The front facade has a differen hierarchical structure than the side First hierarchy Second hierarchy Third hierarchy

facades. In the front facade the hierarchy is constructed through the columns whereas in the side facades the hierarchy is constructed through the horizontal detailing.

30

Southeast facade 1:2000

Northeast facade 1:2000

3.3.5 Composition of the facade - hierarchy

First hierarchy Second hierarchy

Similar to the Altes Museum, the hierarchic element of the Altes Museum is the a roof element. Subhierarchic to this are the columns.

31

[WHY]

South facade - 1:2000

3.3.6 Composition of the facade - similar proportions

“Proportion is the relation of height to width.” (Durand, 1802) Similar proportions are found that occur in both buidings.

Roughly speaking in both building the facades can be divided in three vertical faces.The proportion of the outer faces appears to be equal to each other. Each building has a striking element that rises above the structure.

In Altes Museum this is the top of the dome, in Neue Nationalgallery this Proportions

is the upper floor. These volumes appear to have equal proportions in the facade.

Durand, J. N. (1802). Précis of the Lectures on Architecture. Section Three. Forms and Proportions.

32

Southeast facade 1:2000

Northeast facade 1:2000

33

Ground floor - 1:2000

Repetition

Section A - 1:2000

Section B - 1:2000

3.4.1 Order or spaces - repetition and variation

The Altes Museum is designed from a system of walls, consequently resulting in a repetition of plan in all three floorplans. However, when anaVariation 1 Variation 2 Variation 3

lyzing the section, it appears that even though the rooms are repeated, they vary in ceiling height, creating different dimensions of rooms at each floor. It has repetition in plan but varies in section.

34

Section A - 1:2000

Section B - 1:2000

Repetition 1 Repetition 2

Section A - 1:2000

Section B - 1:2000

3.4.1 Order or spaces - repetition and variation

The Neue Nationalgallerie is designed from a grid to create a flexible space and a free floorplan. This creates the oppertunity for variation.

The repetition in the Neue Nationalgallerie is found in its shape. The top volume of the gallery is repeated in both section and elevation, whereas Variation

the basement floor varies in dimension.

35

Section A - 1:2000

Section B - 1:2000

3.4.2 Order or spaces - rhythm

Rhythm “is movement or procedure with uniform or patterned recurrence of a beat, accent, or the like.”. (Dictionary, 2016) The rhythm is given through the repetition of rooms, though not equal in Rhythm

size, they are equally placed at each side of a symmetry axis.

Rhythm. (2016, 06 27). Retrieved from Dictionary: http://www.dictionary.com/browse/ rhythm

36

A

B

Basement - 1:2000

Section A - 1:2000

Section B - 1:2000

3.4.2 Order or spaces - rhythm

For the Neue Nationalgallerie it is more difficult to define a rhythm. The volume on top appears as a single tone, and due to the flexible plan, the tones are spread over the basement floor. Yet, similarities n the rhythm Rhythm

are found through the axis of symmetry.

37

Ground floor - 1:2000

3.4.3 Order or spaces - symmetry

Symmetry “is the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts.” (Dictionary, 2016) The plan shows one main axis of symmetry, giving absolute symmetry in the plan. In the other direction, two smaller segments are found to have Symmetry

symmetry in themself.

Symmetry. (2016, 06 27). Retrieved from Dictionary: http://www.dictionary.com/browse/ symmetry?s=t

38

A

B

Ground floor - 1:2000

A

B

Basement - 1:2000

3.4.3 Order or spaces - symmetry

The upper floorplan shows two axis of symmetry, due to the cubic shape.

Symmetry

In the lower floorplan a shifted symmetry is detected.

39

Section A - 1:2000

Section B - 1:2000

3.4.3 Order or spaces - symmetry

In section a similar story can be told. Due to the symmetry axis in the Symmetry

oor plan, the section appears to have an absolut symmetry as well.

Again, the rotunda of the building has more symmetry axices.

40

Section A - 1:2000

Section B - 1:2000

3.4.3 Order or spaces - symmetry

Symmetry

In section symmetry appears only in the upper floor.

41

Ground oor - 1:2000

3.5 Geometry

By means of a geometry analysis it is tried to understand whether similar dimensions or hidden design principles are used to compose the building.

In the plan of the Altes Museum, the dimension of the rotunda appears to relate to the width and length of the inner block. The width is twice Geometry 1 Geometry 2 Geometry 3

the size of the outer dimensions of the Rotunda (including wallthickness), whereas the length is four times the size of the inner dimensions of the Rotunde (excluding wallthickness).

42

A

B

Ground oor - 1:2000

A

B

Basement - 1:2000

3.5 Geometry

By means of a geometry analysis it is tried to understand whether similar dimensions or hidden design principles are used to compose the building.

The design of the Neue Nationalgallery is based on a grid, bringing forGeometry

ward clear rectangular shapes in plan.

43

Section A - 1:2000

Section B - 1:2000

3.5 Geometry

By means of a geometry analysis it is tried to understand whether similar dimensions or hidden design principles are used to compose the building.

Geometry 1 Geometry 2 Geometry 3

In the section of the Altes Museum it appears that the dimensions of the Rotunda as found in the plan, also exist in the section, as it is eqally high as it is in width.

44

Section A - 1:2000

Section B - 1:2000

3.5 Geometry

The Neue Nationalgallery knows a clear rectangular geometry. The Geometry 1 Geometry 2

topvolume is recognized in both sections, resting on a base, the basement oor.

45