The French word for "oval" comes from ovum, which means an egg in Latin. In geometry, an oval is understood as a flat convex closed curve, and the simplest examples of an oval are a circle and an ellipse. By the way, the egg has the shape of an ovoid - a curved convex closed line with one axis of symmetry.
It is necessary
- - paper;
- - pencil;
- - calculator;
- - eraser;
- - ruler;
- - pattern;
- - compasses.
Instructions
Step 1
Circle Select the size that the circle will have - this is called the diameter. The size of the diameter in the circle is constant. Divide it by 2. This is the radius of the future circle.
Step 2
Set the compass opening equal to the radius, then draw a circle: stick the point of the compass into the paper and rotate the compass 360 degrees around its axis.
Step 3
Ellipse The elements of an ellipse have mathematical definitions and there is a clear relationship between all the elements. We are talking about focal, perifocal and apofocal distances, focal parameter and radius, major and minor semiaxis. Therefore, the construction of an ellipse will become much clearer with knowledge of this section of geometry.
Step 4
Method One Draw two perpendicular straight lines on paper using a ruler. These will be the axes of symmetry.
Step 5
Place the leg of the compass at the intersection of the axes A (this will be the center of the ellipse) and mark points B and C on the horizontal axis with one radius, and then on the vertical axis, but with a different (smaller) radius - points D and E. Points B, C, D and E are the vertices of the ellipse. Segments AB and AC are semi-major axes of the ellipse, AD and AE are small.
Step 6
Make notches on the horizontal axis by placing the leg of the compass with the solution AD = AE (semi-minor axis) alternately at points B and C. These will be points F and G - the foci of the ellipse, and the segment FG - the focal length.
Step 7
Select an arbitrary point H on the segment BC. Draw a circle with radius BH from the center at point F and a circle with radius CH from the center at point G. The intersection of these circles are the points of our ellipse.
Step 8
Repeat the actions listed in the previous paragraph, choosing another point H1, H2, H3 and so on on the BC segment, until the points acquire a distinct oval outline. Connect the constructed points using a piece.
Step 9
Method Two Draw with a compass two circles of different diameters with one center lying at the intersection of the axes of symmetry. The diameter of the larger circle along the horizontal axis and the diameter of the minor axis along the vertical axis are the vertices of the ellipse.
Step 10
Calculate the length of the larger circle (3, 14 times the diameter) and divide it by an equal number of N.
Step 11
Break the large circle into N equal pieces. Using a compass (the opening of the compass is equal to the value calculated in the previous paragraph), make notches on the great circle, starting from the point of its intersection with the horizontal axis. Draw lines through the center of the circles and serifs. Thus, both circles will be split into equal parts.
Step 12
Draw horizontal lines through the points of intersection of these lines with the small circle (except for the points at 12 and 6 o'clock).
Step 13
Omit vertical lines from all serifs on the larger circle (except for the 12, 3, 6, and 9 o'clock points).
Step 14
Connect all the points of intersection of the horizontal lines with the perpendiculars of the smooth curve using patterns. The intersection points of the contour lines drawn from the points of the small circle and the verticals drawn from the points of the large circle form an oval in the form of an ellipse.
