Geometrical Constructions 1 Academic Year 2018/19 1st (fall) semester

2 ND DRAWING

Tint-drawing, size A2 (594 mm x 420 mm) Deadline: 30th November 2018 Late submission: 14th December 2018

The maximum result of the drawing is 15 points, the minimum to gain is 7.5 points. In case of late submission, the result will be reduced by 3 points. Drawings after the late submission deadline are not acceptable. The arrangement of the drawings is arbitrary but should be composed to have a pleasant overall picture with the titles. Please use the notations of the lecture notes. Titles of the figures are italic.

Please do not forget about the formal requirements. Moreover, the reference lines, the direction of affinity, etc. (i.e. all the lines connecting a point to its image) should be dashed lines.

1) Construct an equilateral with sides of 5 cm. Translate the triangle along one of its symmetry axes by one third of its height. Apply point reflection on both with respect to an arbitrary external point. Hatch the original triangle lighter, the three others darker. (TRANSLATION AND POINT REFLECTION)

2) Construct a whose sides are of 8 cm. Rotate it by a) +30° (if your Neptun-code starts with A-M) b) -30° (if your Neptun-code starts with N-Z) about the center and at the same time apply homothetic transformation on it so that the vertices of the image of the square lie on the sides of the original square. Repeat the process at least 5 times. (ROTATION)

3) Construct a regular heptagram if its Schläfli symbol is a) {7/2} (if your Neptun-code starts with A-M). b) {7/3} (if your Neptun-code starts with N-Z). Reflect the heptagram with respect to an axis which passes through two adjacent vertices lying on the circumscribed of the heptagram. The radius of the is of 4 cm. Hatch the original heptagram lighter, the result darker. (AXIAL REFLECTION)

4) Construct a “paw” according to the figure attached below. Apply glide reflection on it whose axis is the dashed line being 33 mm far from the center of the biggest circle. The length of the translation vector is of 8 cm. (GLIDE REFLECTION)

5) Construct a whose sides are of 3 cm. Apply homothety on it. The center is the midpoint of one of the smaller diagonals and its scale factor is λ = -2. (HOMOTHETY)

O:\2018-2019-1\e-GCon1\Drawings\GC1_drawing2_2018_fall_ver2.doc 6) Construct a regular . The radius of its circumscribed circle is 5 cm. Apply orthogonal affinity on the pentagon so that the axis passes through its midpoint O and the image of a is between the axis and the original point. Hatch the transformed pentagon. (ORTHOGONAL AFFINITY)

7) An arbitrary and a line is given. Apply axial affinity on the parallelogram so that its image is a square and the axis of the affinity is the given line. (OBLIQUE AFFINITY)

8) The radius of the circumscribed circle of a regular pentagon is of 5 cm. Construct the image of it if the central collineation is given by a center which lies on one of its symmetry axis and the axis of the transformation is parallel to one of its sides as well as intersecting the pentagon. Hatch the transformed pentagon. (CENTRAL COLLINEATION)

9) The central collineation is given by the axis, a vanishing line and the center. Construct a regular hexagon whose sides are of 3 cm. Its center lies on the axis and a pair of sides is perpendicular to the axis. Construct two other which are attached to the original hexagon and to each other like tiles and have one common vertex. Construct the perspective image of the tiles, and hatch the result (the three perspective hexagons should be hatched with different directions). (PERSPECTIVE IMAGE)

30th October 2018, Budapest

Johanna Pék Ph.D. Senior Lecturer

István Makai Instructor

Figure for exercise 4: