The document discusses the golden ratio and its applications in design. It begins by defining the golden ratio mathematically and explaining its historical study. Architects have incorporated the golden ratio in structures like the Parthenon and Great Pyramid because it is visually appealing. The document outlines design processes and considerations for interior spaces like kitchens, dining rooms, bedrooms, and bathrooms. Elements, dimensions, materials, and relationships between spaces are addressed.

1. GOLDEN RATIO
DESIGN
PROCESSES
DESIGN CRITERIA

2. INTRODUCTION
 In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of
their sum to the larger of the two quantities. The figure on the right illustrates the geometric
relationship. Expressed algebraically, for quantities a and b with a > b > 0,
 The golden ratio is also called the golden mean or golden section .Other names include
extreme and mean ratio, medial section, divine proportion, divine section , golden proportion,
golden cut, and golden number.
 Some twentieth-century artists and architects, including Le Corbusier and Dalí, have
proportioned their works to approximate the golden ratio—especially in the form of the
golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—
believing this proportion to be aesthetically pleasing. The golden ratio appears in some
patterns in nature, including the spiral arrangement of leaves and other plant parts.
 Mathematicians since Euclid have studied the properties of the golden ratio, including its
appearance in the dimensions of a regular pentagon and in a golden rectangle, which may
be cut into a square and a smaller rectangle with the same aspect ratio. Aesthetics
Architecture Painting Book design Design Music Nature
 A golden rectangle(in pink) with longer side (a) and shorter side (b), when placed adjacent
to a square with sides of length a, will produce a similar golden rectangle with longer side a
+ b and shorter side a. This illustrates the relationship

3. HISTORY
• The golden ratio has been claimed to have held a special fascination for at least 2,400 years, although without reliable evidence.
According to Mario Livio:
• Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian
mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as
Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the
Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even
mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has
inspired thinkers of all disciplines like no other number in the history of mathematic
• Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The
division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and
pentagons. Euclid's Elements provides the first known written definition of what is now called the golden ratio:
• A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the
greater to the lesser.

4. ARCHITECTURE
• The Parthenon is a former temple in Acropolis, Greece. This
temple is dedicated to goddess Athena. The construction of the
temple embarked in 447 BC. Similar to many other temples
in Greece, the design of ‘The Parthenon’ is also in such a way,
to be seen only from outside. It is also called as facade
architecture. Naturally, golden ratio or the golden rectangle
concept is used which is seen in the figure. It is very appealing
and pleasing to our human eyes. Some experts also say that
this construction had unknowingly used the concept of golden
ratio which again highlights that it is the most stable
architectural configuration.
• Similarly, the Great Pyramid of Giza's dimensions are also
based on the Golden Ratio. If we take a cross section of the
Great Pyramid, we get a right triangle, the so-called Egyptian
Triangle.

5. IN MODERN ARCHITECTURE
• Modern architects take advantage of golden ratio. They find that it is highly
appealing to our eyes. More importantly the mathematics behind it provides a
proper balance for the entire constructional system. As stated above, the golden
ratio gives various options for construction. It can be used as a rectangle or a
polygonal construction. This is very prevalent in traditional and cultural
countries. But modern buildings in Japan, Singapore and some European nations
are spiral architectures, which have used the golden spiral. India’s richest man,
Mukesh Ambani’s official modern residence in the city of Mumbai was constructed
with the very same idea of golden ratio that was used in the ancient
architectures.

6. NATURE
•
The concept of golden ratio is already there in the
nature. For this reason, the golden ratio is
also called as divine ratio which is a direct
reference to the existence of god. The most
pertinent example is found in Sunflower. The
arrangement of the seeds of the Sunflower is a
spiral curve or the golden curve. Scientists call
this arrangement as a physically stable one and
visually appealing one. The seeds are intact to
each other. This is to prevent the seeds detaching
from the flower by experiencing only an iota
current of air. If we magnify this visionary million
times, we will find that, even our galaxies in this
universe are spiral in shape. It is not a normal
spiral. As mentioned above, it is the divine spiral.
Similarly, it is also found in the face of human
beings, ears of certain animals and also in
plethora of flora and fauna.
•

7. DEFINATION
• Golden ratio, also known as the golden section, golden mean, or
divine proportion, in mathematics, the irrational number (1 +
Square root of√5)/2, often denoted by the Greek letter ϕ or τ,
which is approximately equal to 1.618.

8. DESIGN PROCESSES

9. Step 1 – Identify the Problem: A design is always based on a need. Gathering additional information clarifies the
problem and establishes limitations that must be taken into account. Designers need to know the budget for each
portion of the design. This serves as a realistic limit for what can be included.
Step 2 – Generate Preliminary Ideas: Preliminary ideas are initial thoughts generated by architects regarding
possible solutions to the design problem. Preliminary ideas are often recorded as sketches. Some preliminary ideas
are recorded in list form. The goal is to record all ideas so none are forgotten as the design process proceeds.
Step 3 – Refine Ideas: When the idea is refined, the sketch is converted into a scale drawing. This helps determine
if the idea is workable. Elements from two or more preliminary ideas might be combined to create a workable
solution.
Step 4 – Analyze Ideas: Structural analysis examines the strength requirements of the structure.
Site analysis: is an analysis of how the proposed building will fit on a site. The location of the main entrance,
driveways, parking lots, and other facilities will be studied.
Functional analysis: determines if a design will work as planned.
Cost Analysis: Once the analysis of the various design ideas is completed, the architects prepare their ideas for
presentation to their clients.
Step 5 – Select the Design: Based on the analysis, the architects decide which design alternatives to present to the
client. If the client chooses to continue with the project, the architects will be authorized to prepare construction
documents.
Step 6 – Prepare Construction Documents: Once a design is chosen detailed, dimensioned drawings of every part of
the building are prepared. Specifications for materials and construction methods to be employed are also
prepared.
Step 7 – Implement Design: This includes all the activities in completing the project, from managing the project to
closing the contract and transferring the project. The first step is to hire contractors so work may begin. The
design architects are often hired by the client to oversee the work being done by each contractor in the project.

10. DESIGN CRITERIA
• Location
• Orientation.
• Function
• Area and dimensions. -Furniture included.
• Circulation.
• Materials and colors used for different space elements.
• Style of design.
• Temperature/Humidity
• Daylight / Ventilation

11. DESIGN CRITERIA
Function, appearance, cost, strength, and materials. All factors are interrelated.
Function: The design solution must meet the needs of the design problem. For example, a garage must be
large enough for the vehicles that are to be parked in it.
Appearance: Bothe the exterior and interior of the building should be attractive.
Cost: A project cannot be built if the cost exceeds the money available for construction. The architect
develops an initial budget, dividing the total amount in categories: foundation, structure, roof and exterior
walls, interior partitions and ceiling, mechanical, electrical, interior finish, and landscaping.
Strength: Foundations must support a building and its contents. Walls, beams, joists, rafters, and all other
structural components must meet design requirements.
Materials: Characteristics such as strength, weather resistance, fire resistance, and resistance to heat
transfer determine if a material will be appropriate for a given use. Appearance is important for visible
material such as drywall, wood paneling or siding, and brick. These materials must be attractive, but also
functional.

12. KITCHEN
• Each interior space has special design criteria in
terms of area, dimensions, furniture, colors,
materials, systems, orientation and relationship
with other interior and exterior spaces.
• Kitchen Location: Close to the entrance and
dining - best orientation is towards East or South
East
• Area : around 10% of house area – worktops
around 18% of kitchen area. Elements: sink,
oven, dish washer, cupboards, dining table,
accessories. Work triangle : sink, oven – should
not be interrupted by any furniture pieces. –
Triangle parameter ranges between 4 – 8 m. –
Each line not less than 1.25 and not more than
2.75
• Durable materials – heavy duty. Ceramic walls
and non- slipping flooring. Dimensions will be
discussed at class 6

13. DINING ROOM
• DINING ROOM Location:
close to the kitchen and
reception – orientation to
good views. Natural lighting
is preferred. Elements:
dining table and seats,
Cupboard ( opt.) and
accessories. Suitable colors
and complementary
arrangement. Service
circulation is very
important.

15. BEDROOM
• BED ROOMS Location: –In a
private place. –A way from noise.
–Oriented towards East –
Northern East. Master Bed Room:
Built in bathroom and dressing
room. Other bed rooms:
appropriate furniture and colors
for age and gender. Basic
furniture: beds, cupboards,
mirrors. Avoid beds under
windows. Availability of free
space in the room is essential

16. BATHROOMS
• BATH ROOMS : Location : Very
close to bed rooms and sometimes
is imbedded within the room
Dimension : Depends on design
and area Dimensions for elements
are shown at class by instructor.
Basic Elements : Bathtub, Toilet,
Shower, Cabinets, Accessories.
Accurate location for space
elements. Ceramics for walls and
non- slipping flooring for floors.
Sometimes laundry is included