Geometry in Construction EngineeringLaajuus (5 cr)

Objective

Learning competence
Students are aware of the basic properties of trigonometric functions. They know how to solve rectangular and oblique triangles. They are familiar with the more common plane figures and solid bodies and know how to calculate their areas and volumes. The students are able to perform necessary and sufficiently accurate measurements to calculate areas and volumes, also using scale in calculations.

Working community competence
Students are able to present the stages of geometrical problem solving orally and in writing and also via online and virtual communication. They are competent in graphical illustration of mathematical models. Students are able to function in various groups and teams and to manage teams, which seek solutions for geometrical problems.

Quality management competence
Students are able to apply both exact and approximate methods to determine the correctness of mathematical work. Students know how to estimate the inaccuracy of measurements and take it into consideration.

Content

Trigonometry:
- Trigonometric functions, especially the sine, cosine and tangent.
- Common trigonometric formulae
- Rectangular and oblique triangles and how to solve them

Plane figures:
- Areas of the more common plane figures
- The concept and application of similarity
- Centre of gravity
- Second moment of area, modulus of section
- Scale in area calculations
- Practical measurement exercises related to surface areas, individually or in small groups. Proper reporting of measurement results and calculations.
- Evaluation of the effect of error in measurement results.

Space geometry:
- Common solid bodies: cylinder, cone, truncated cone, ball, and their parts
- Calculating volumes and areas
- Scale in volume calculations
- Practical measurement exercises related to volumes, individually or in small groups. Proper reporting of measurement results and calculations.

Qualifications

Rakennustekniikan algebra.

Assessment criteria, satisfactory (1)

The student is able to solve the sides and angles of a right-angled triangle using the Pythagorean theorem and trigonometric functions. They are able to use the Sine and Cosine rules when calculating an oblique-angled triangle. They master the principles of calculating areas of simple plane figures. They are able to calculate the position of the centroid and moment of inertia of a simple cross section.

Assessment criteria, good (3)

The student is able to apply the solution methods of a right-angled and oblique-angled triangle also in a non-standard problems. They are able to calculate the position of the centroid and moment of inertia of a cross section consisting of arbitrary rectangular parts .

Assessment criteria, excellent (5)

The student is able to apply the solution methods of triangles in practical problems. They master the calculation of the position of the centroid and moment of inertia of a cross sections. The student independently searches for information in different sources and utilizes it in practical problem solving.