P R O G R A M

P R O G R A M

Section 1. MATHEMATICS BOTH ARCHITECTURE – COMPARISON AND ANALYSIS
1. The introduction remarks.
2. "Architectonics" of mathematics.
3. Architecture, from the point of view of mathematics.
4. Interaction of architecture and mathematics in modern conditions.

Section 2. A HISTORY OF MATHEMATICS IN an ARCHITECTURAL RETROSPECT
1. Origin of mathematics and architecture.
2. Architecture and mathematics of ancient Near East.
3. Development of architecture and mathematics of the antique world (Greece and Rome).
4. Architecture and mathematics of ancient India and China.
5. The European architecture and mathematics of the Middle Ages.
6. Prosperity of architecture and mathematical science in epoch of Renaissance.
7. Architecture and mathematics in 18 and 19 cent. A bookmark of bases of modern mathematics
8. Use in modern architecture of mathematical ideas of receptions and methods. Increase of a role of mathematics in architecture and town-planning.

S e c t i o n 3. THE ARCHITECTURAL THEORY OF SETS
1. Sets, elements of set. Designations.
2. Equality and equivalence of sets. Subsets. Empty and universal sets.
3. Sets final and infinite. Paradoxes of the theory of sets.
4. Operations of association and crossing of sets. A difference and a symmetric difference.
5. Natural numbers. Numbers simple and compound. Set of integers. Integers in architecture.
6. Rational and irrational numbers. Set of real numbers.
7. Numerical ratio in architecture. The module of the architectural object. The relation « of Gold SECTION».
8. Application set’s methods by development of architectural compositions. Set-multiple methods in architecture, design and town-planning.

Section 4. SPACE IN MATHEMATICS AND ARCHITECTURE
1. Axioms of mathematical space. Concept of dimension of Space of different dimensions.
2. Concept about system of coordinates. Coordinates on a straight line and planes. The Cartesian system of coordinates in 3-dimensional space.
3. Some properties Euclid’s space: boundlessness, infinity.
4. Concept of symmetry. Symmetry of spaces. External and internal properties of spaces.
5. Euclid’s space – model of a real physical space. Perception and documenting of mathematical space.
6. Concept of an architectural space. Real and psychological making architectural space. Features of perception and documenting of an architectural space by a man.
7. The comparative analysis of properties of space in architecture and mathematics.

Section 5. LINES BOTH SURFACES IN MATHEMATICS AND ARCHITECTURE
1. Concept of a line. The equation of a line. A straight line on a plane. Broken lines.
2. Transformations of a plane. Lines of the 2-nd order. Some remarkable lines on a plane. The common theory of flat curves. Topological classification of curves on a plane. Flat lines in architecture. Patterns, ornaments and invoices.
3. Concept of a surface. The equation of a surface. A plane. A mutual arrangement of planes. Surfaces of the second order.
4. The general theory of surfaces. Elements of topology. Some remarkable surfaces. Membranes and minimal surfaces. Features of visual perception of surfaces. Surfaces in architecture and town-planning
5. The equations of lines in space. Straight lines in space. A mutual arrangement of straight lines and planes. The general theory of spatial curves. Natural equations of a curve.
6. Some remarkable spatial curves. Spatial curves in mathematics art and in architecture.

Section 6. SYMMETRY in MATHEMATICS AND ARCHITECTURE
1. Concept of symmetry. Kinds of symmetry: reflection, turn, carry.
2. Elements of the theory of groups. Groups of symmetry. Symmetry in nature, science, art.
3. Traditions of symmetry in design, architecture and town-planning.
4. Use of methods of abstract algebra at solution of architectural and town-planning tasks.

Section 7. THE ARCHITECTURAL THEORY OF PROBABILITIES
1. Definitions and basic concepts of the theory of probabilities.
2. The theorems and formulas of the theory of probabilities. Repeated independent tests. The limiting theorems. Discrete and continuous casual sizes.
3. Definitions and basic concepts of mathematical statistics. Dot and interval estimations. Check of statistical hypotheses. Criteria of the consent.
4. Use of probabilities’ and statistics’ methods in architectural and town-planning designing

Section 8. THE ARCHITECTURAL THEORY GRAPHS
1. Concept of graphs. The basic definitions and theorems. A task about Keningsberg’s bridges.
2. Trees and cycles. Connection of cities. Streets and areas. The focused columns. The flat graphs.
3. Correct polygons and mosaic. A task about painting of maps.
4. Use graphs at the solution of architectural tasks.

Section 9. MATHEMATICAL METHODS OF DEFINITION OF AESTHETIC VALUE OF AN ARCHITECTURAL COMPOSITION
1. An integrated estimation of beauty of architectural object
2. A surface of beauty. An estimation of a volume-spatial composition.
3. An aesthetic estimation of architectural environment.
4. A flow of beauty on a direction and dot aesthetic estimation. Function of beauty.
5. An integrated of a beauty of an architectural environment.

Section 10. MATHEMATICAL METHODS IN A SCIENCE, ENGINEERING AND ART.
MATHEMATICS AS A METALANGUAGE OF AN EXISTENCE

If it is necessary it is possible to include additional sections, as for example: Architectural computer science, Linear algebra, Basis of optimization and etc.