Le Corbusier

Le Corbusier's modern architectural system is structured upon four revolutionary paradigms:

• The Dom-Ino Reinforced Concrete Skeleton (1914): Structural decoupling of load-bearing support from enclosure, utilizing point-loaded reinforced concrete columns and flat slabs with cantilevered perimeters.
• The Five Points of a New Architecture (1926): Systematic derivation of architectural morphology enabled by the Dom-Ino frame: 1. Les pilotis (reinforced concrete ground stilts). 2. Le toit-jardin (flat roof garden / terrace). 3. Le plan libre (free plan / non-structural interior walls). 4. La fenêtre en longueur (horizontal ribbon window). 5. La façade libre (free facade / non-structural curtain envelope).
• The Modulor Anthropometric Scale (1948): Proportional measurement scale linking the ergonomic dimensions of the human body to the Golden Ratio ($\phi \approx 1.618$) and the Fibonacci series.
• Béton Brut (Material Honesty): Exposure of raw, unfinished cast concrete bearing the imprinted grain of wooden formwork, founding the Brutalist movement.

+--------------------------------------------------------------+
|               DOM-INO STRUCTURAL FRAME (1914)                |
|                                                              |
|        [ Flat Reinforced Concrete Roof Slab ]                |
|           |                      |                      |    |
|           | (Reinforced          | (Reinforced          |    |
|           |  Concrete Column)    |  Concrete Column)    |    |
|           |                      |                      |    |
|        [ Intermediate Floor Slab (Cantilevered Edges) ]      |
|           |                      |                      |    |
|        [ Pilotis Ground Columns (Zero Load on Ground Encl.)] |
|                                                              |
|     Consequence: 100% Free Plan + 100% Free Glass Facade     |
+--------------------------------------------------------------+

2.1 The Mathematics of the Modulor (1948)

The Modulor establishes two interlaced geometric progressions (the Red Series and the Blue Series) based on a standardized human height $H_0 = 183\text{ cm}$ (approx. 6 feet) and the Golden Ratio $\phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887$:

• Key Body Reference Thresholds:
• Solar plexus / Navel height: $H_{\text{navel}} = \frac{H_0}{\phi} = \frac{183}{1.618} \approx 113\text{ cm}$
• Total reach height with raised hand: $H_{\text{reach}} = 2 \cdot H_{\text{navel}} = 226\text{ cm}$

The Red Series (Scaling from $H_{\text{navel}} = 113\text{ cm}$):

$$R_n = 113 \cdot \phi^n \quad (n \in \mathbb{Z})$$ $$\dots, 16, 27, 43, 70, 113, 183, 296, 479\text{ cm}, \dots$$ Notice that $70 + 43 = 113$ and $113 + 70 = 183$ (Fibonacci additive property).

The Blue Series (Scaling from $H_{\text{reach}} = 226\text{ cm}$):

$$B_n = 226 \cdot \phi^n \quad (n \in \mathbb{Z})$$ $$\dots, 13, 20, 33, 53, 86, 140, 226, 366, 592\text{ cm}, \dots$$ Notice that $86 + 140 = 226$ and $226 / 2 = 113$ (Red Series link).

2.2 Brise-Soleil Solar Shading Geometry

To eliminate excessive solar heat gain through curtain walls, Le Corbusier engineered the brise-soleil (concrete sun-breaker baffles). The horizontal projection depth $D$ and vertical spacing $S$ of louvers are governed by the solar altitude angle $\alpha$ and azimuth $\beta$ at the summer solstice: $$D = S \cdot \frac{\cos\beta}{\tan\alpha}$$ Ensuring 100% shade during high summer sun ($\alpha > 60^\circ$) while admitting low winter solar heat ($\alpha < 30^\circ$).

3.1 Villa Savoye Sectional & Functional Topology (1929)

        =================== ROOF LEVEL ===================
        [ Solarium Curve ]       [ Roof Garden / Terrace ]
        =================== FIRST LEVEL ==================
        [ Ribbon Window ]  [ Grand Living Salon ]  [ Ramp ]
        [ Strip Glazing ]  [ Non-loadbearing Bedrms]  |
        ================== GROUND LEVEL ==================
        (Pilotis Stilts)   [ Glazed Semi-Circular Arc ] |
             |             [ Chauffeur Quarters / Garage]
             |             (Turn radius: 1927 Citroën car)
        =================== BASEMENT =====================

3.2 Unité d'Habitation Interlocking Duplex Apartment Cross-Section

   +-----------------------------------------------------------+
   |   Apartment A: Upper Level (Living Room - Double Height)  |
   +-----------------------------+-----------------------------+
   |   Apartment A: Lower Bedrm  |   CENTRAL INTERIOR STREET   |
   +-----------------------------+ (Shopping / Services Fl. 7) |
   |   Apartment B: Upper Bedrm  |                             |
   +-----------------------------+-----------------------------+
   |   Apartment B: Lower Level (Living Room - Double Height)  |
   +-----------------------------------------------------------+
   (Cross-ventilation through entire building slab: 24m depth!)

• Villa Savoye (1928–1931): Embodied all Five Points with reinforced concrete pilotis on a $4.75\text{ m} \times 4.75\text{ m}$ grid; listed as a UNESCO World Heritage site in 2016.
• Unité d'Habitation Acoustic and Modular Scale (1952): Realized 337 modular apartments in Marseille using 15 distinct Modulor dimensions, achieving high-density communal living with internal sound-isolation lead plates between party walls.
• Chandigarh High Court Canopy (1956): Constructed a 140-meter-long continuous concrete parasol roof with a 12-meter cantilever, creating an artificial microclimate that reduced interior building temperatures by up to $8^\circ\text{C}$ without mechanical air conditioning.
• Ronchamp Acoustic Shell: Cast a reinforced concrete roof slab with an upward concave curve mimicking a crab carapace, resting on point pins above the perimeter walls, leaving a 10 cm light gap that makes the 2,000-ton concrete roof appear to float.

5.1 Thermal Bridging and Weatherproofing Failures of Early Flat Roofs

Villa Savoye suffered from catastrophic water leaks, condensation, and cold drafts within months of completion. The Madame Savoye threatened legal action over the uninhabitable roof terrace leaks, uninsulated concrete thermal bridges, and cracked skylights, requiring decades of modern restorative waterproofing.

5.2 The Radiant City Urban Monoculture Pathology

Le Corbusier's Plan Voisin (1925), which proposed demolishing two square miles of historic central Paris to erect eighteen 60-story cruciform office skyscrapers in an open park, underestimated the social value of human-scaled streets. When adopted by post-war urban planners (e.g. Pruitt-Igoe in St. Louis), Corbusian superblocks frequently degenerated into social isolation, transit deserts, and economic blight.

5.3 Modulor Anthropometric Bias

The Modulor was based exclusively on the height of a tall Caucasian male ($1.83\text{ m} / 6\text{ ft}$), arbitrarily selected based on British detective fiction standards. The scale failed to account for women, children, elderly individuals, or populations with different median anthropometric statures.

• Vers une architecture (Toward an Architecture), Éditions Crès, Paris, 1923.
• Urbanisme (Urbanism / The City of Tomorrow), Éditions Crès, Paris, 1925.
• Les 5 points d'une architecture nouvelle (with Pierre Jeanneret), L'Architecture Vivante, Paris, 1927.
• Précisions sur un état présent de l'architecture et de l'urbanisme, Crès, Paris, 1930.
• Le Modulor: Essai sur une mesure harmonique à l'échelle humaine, Éditions de l'Architecture d'Aujourd'hui, Boulogne, 1948.
• Modulor 2: La parole est aux usagers, Éditions de l'Architecture d'Aujourd'hui, 1955.
• Le poème de l'angle droit (Poem of the Right Angle), Tériade, Paris, 1955.