Science in the drawing geometry? This topic is somewhat a bit confusing, so to make things simpler we will consider a example.
Example: Given ΔABC, the height AH, median AM (H and M on BC).
Very simple, isn’t it? Then how will we draw such a figure? We can draw as below:
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| Figure 1: Triangle ABC, the height AH, the median AM |
It is absolutely accurate according to the original data. The problem here is that points M and H are too close together, and that will lead to difficulty to distinguish between them and between two lines AH and AM, making simple drawing become unrecognizable.
What if after that, we need to identify the circumcenter and center of gravity of ΔABC? In this case, we can say Figure 1 is "not scientific". In general, it would be a lot better if drawing like Figure 2 below:
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| Figure 2: Triangle ABC, the height AH, the median AM |
Similarly, it can be noticed that Figure 3 or Figure 4 below are not scientific (except for cases that are required to draw as such):
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| Figure 3: Triangle ABC, the height AH, the median AM |
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| Figure 4: Triangle ABC, the height AH, the median AM |
So to draw scientifically, what do we have to note? The following suggestions may be helpful and should be applied when you start drawing (if not bound by other facts):
1) When drawing angles or triangles, try not to draw the vertices with special values, such as 30°, 60°, 45°, 90°, 120°, 180°, ...
2) The edges of the triangles, parallelograms or rectangle should not be drawn approximately equal. For example, if you draw a rectangle ABCD, the lengths of AB and BC should not be close in value and also one should not double the other!
3) If you draw a trapezoid or a triangle, you should not draw an isosceles one. Normally, the two trapezoidal sides should be approximately 1/3 different in lengths. For example, the trapezoid ABCD, AB // CD, you should draw the side BC = about 2/3 or 4/3 of the DA.
4) Use the solid or interrupted lines logically. For example, if two sides of a triangle are in solid lines, the 3rd edge should be also be solid. Or when you have multiple solid lines converge at one point, then an additional line should be an interrupted line...
There may be many other points to note, but the above points have helped a great deal. Most importantly, the figure should be easy to read, easy to understand and highlight the given facts as well as the relationships between them.
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9.2.2014
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