# Descriptive Geometry

## Course Description:

Learning of descriptive methods (two-dimensional representations of three-dimensional objects constructed following mathematical rules), geometric knowledge enrichment, deepening of the geometrical perception, sharpening of the mathematical thought and especially of the geometrical thought, graphical solutions of technical problems, facilitation of the understanding of computer generated technical drawings.

### Prerequisite Knowledge

Basic knowledge of Euclidean Geometry.

### Course Units

# Title Description Hours
1 Stereometry Basic notions: points, lines, planes, angles (dihedral, trihedral, polyhedral) and their measurement, perpendicularity, parallelism, skew lines, projections (perpendicular, lateral, central), distances, slopes, areas, volumes, the three- perpendiculars Theorem, Thales’s Theorem, prisms, pyramids, cylinders, cones, spheres, basic propositions. 3Χ3=9
2 Descriptive Geometry in two planes Relative positions of points, lines and planes, inclinations and declinations, true lengths, trace lines, measures, developments. Technical applications: plane intersections of solids, solid intersections, cylindrical helices-turning stairs. 5Χ3=15
3 Descriptive Geometry in one plane via altitudes Slopes, steps, trace lines, relative positions of points, lines and planes, measurements, unwrappings. Technical applications: roofs, topographic maps, tunnels, cuts and fills of technical works (bankings).

### Learning Objectives

After successfully completing the lesson’s requirements, students will be able to: 1. realize the exceptionally important position of geometry in the knowledge asset of their profession, 2. think geometrically, and to cover with only a minimal amount of effort any gaps in their geometric knowledge from their secondary or higher education, 3. understand that all technical drawings follow mathematical rules, 4. represent three-dimensional objects via two-dimensional drawings (in more than one way), 5. solve via graphical but mathematical methods those space problems regarding measurement and incidence in technical drawings, 6. work mathematically in certain technical applications.

### Teaching Methods

 Teaching methods Theoretical lectures in class. Solutions in class of examples, problems and exercises solutions in class. Blackboard presentations, use of physical models, use of a projector. Unsolved exercises on the blackboard and in the webpage of the course for personal occupation and knowledge deepening (no formal grading).

### Student Assessment

• Final written exam: 70%
• Mid-term exam: 30%

### Textbooks - Bibliography

1. Electronic notes by the professor: • Solid Geometry• Descriptive Geometry in one plane • Descriptive Geometry in two planes (all in greek)
2. Exercises and past exam-papers (all in greek)
3. «Παραστατική Γεωμετρία», Στ. Μαρκάτης, Αθήνα 2010. (in greek)
4. «Στοιχεία Παραστατικής Γεωμετρίας, Τόμος ΙΙ», Γ. Λευκαδίτης, Αθήνα, 2008. (in greek)
5. «Στοιχεία Παραστατικής Γεωμετρίας, Τόμος Ι», Γ. Λευκαδίτης, Αθήνα, 2003. (in greek)
6. «Μέθοδοι Παραστάσεων, αξονομετρία, υψομετρία, σκιαγραφία», Γ. Λευκαδίτης, 2006. (in greek)
7. «Παραστατική Γεωμετρία», Γρ. Φούντας, Αθήνα, 2005. (in greek)
8. «Μαθήματα Παραστατικής Γεωμετρίας», Γρ. Τσάγκας, Θεσσαλονίκη 1994. (in greek)
9. «Μηχανολογικό Σχέδιο και Στοιχεία Παραστατικής Γεωμετρίας», Στ. Μαυρομάτης, Αθήνα 2003. (in greek)

## Lecture Time - Place:

• Tuesday, 11:45 – 14:30,
Rooms:
• Αμφ. 1/2
• Tuesday, 14:45 – 16:30,
Rooms:
• Αμφ. 1/2

© 2017 School of Civil Engineering, ΕΜΠ