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Grootte: 1622
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Grootte: 1630
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| Verwijderingen worden op deze manier gemarkeerd. | Toevoegingen worden op deze manier gemarkeerd. |
| Regel 3: | Regel 3: |
| Regel 7: | Regel 10: |
| A Reuleaux triangle is characterized as a "curve of constant width". This means that when you place the triangle between two parallel lines, touching the triangle, the distance between the lines will not change when you rotate the triangle. About the points: |
A Reuleaux triangle is characterized as a "curve of constant width". This means that when you place the triangle between two parallel lines, touching the triangle, the distance between the lines will not change when you rotate the triangle. About the points: |
| Regel 14: | Regel 18: |
| Regel 15: | Regel 20: |
| Regel 16: | Regel 22: |
| * DA = 2*DH = sqrt(3)/3. * AH = 3*DH = sqrt(3)/2. * FH = 1 - AH = 1-sqrt(3)/2. |
* DA = 2*DH =sqrt(3)/3. * AH = 3*DH =sqrt(3)/2. * FH = 1-AH =1-sqrt(3)/2. |
| Regel 20: | Regel 27: |
| * Circumscribed radius = DA = sqrt(3)/3 = 1/sqrt(3). * Inscribed radius equilateral triangle = DH = sqrt(3)/6. * Inscribed radius Reuleaux triangle = DF = 1-sqrt(3)/3 = 1-1/sqrt(3). |
* Circumscribed radius = DA =sqrt(3)/3 =1/sqrt(3). * Inscribed radius equilateral triangle = DH =sqrt(3)/6. * Inscribed radius Reuleaux triangle = DF =1-sqrt(3)/3 =1-1/sqrt(3). |
| Regel 24: | Regel 33: |
| The base output in a LISP supporting CAD system, is a closed 2D-polyline containing three arc segments. | The base output in a LISP supporting CAD system, is a closed 2D-polyline containing three arc segments. |
Theory
Back to school for some principles. See https://en.wikipedia.org/wiki/Reuleaux_triangle for it. Reuleaux triangles are used for drilling square holes. In mechanical engineering, the priciples of square motion are possible - amongst others - by using Reuleaux triangles.
- Red and green: x- and y-axis.
- Magenta: equilateral triangle.
- Cyan: Construction circles.
- Blue: Reuleaux triangle
A Reuleaux triangle is characterized as a "curve of constant width". This means that when you place the triangle between two parallel lines, touching the triangle, the distance between the lines will not change when you rotate the triangle. About the points:
- D: The center of the magenta equilateral triangle.
- A, B, C: Corners. Distance AB = BC = AC = 1.
- E, F: The quadrants of one of the three equal cyan circles that can be used to create the triangle, Distance EF = 2.
- F: Point between B and C on Reuleaux triangle.
- H: Point between B and C on equilateral triangle.
In the given situation we can say something about distances (in spreadsheet notation):
- DH =sqrt(3)/6.
- DA = 2*DH =sqrt(3)/3.
- AH = 3*DH =sqrt(3)/2.
- FH = 1-AH =1-sqrt(3)/2.
With a given base size of 1 we can say something about the inscribed and circumscribed circles of both triangles:
- Circumscribed radius = DA =sqrt(3)/3 =1/sqrt(3).
- Inscribed radius equilateral triangle = DH =sqrt(3)/6.
- Inscribed radius Reuleaux triangle = DF =1-sqrt(3)/3 =1-1/sqrt(3).
What you get
The base output in a LISP supporting CAD system, is a closed 2D-polyline containing three arc segments.