This is the write-up of Assignment #5 |
Brian R. Lawler
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EMAT 6680 |
10/21/00
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1. | Centroid. The CENTROID (G) of a triangle is the common intersection of the three medians. | Given 3 points, construct centroid (G). |
9/25/00
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2. | Orthocenter. The ORTHOCENTER (H) of a triangle is the common intersection of the three lines containing the altitudes. | Given 3 points, construct orthocenter (H). |
9/25/00
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3. | Circumcenter. The CIRCUMCENTER (C) of a triangle is the point in the plane equidistant from the three vertices of the triangle. | Given 3 points, construct circumcenter (C). |
9/25/00
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4. | Circumcircle. | Given 3 points, construct the circumcircle of a triangle. |
10/2/00
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5. | Incenter. The INCENTER (I) of a triangle is the point on the interior of the triangle that is equidistant from the three sides. | Given 3 points, construct the incenter of a triangle (I). |
9/25/00
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6. | Incircle. | Given 3 points, construct the incircle of a triangle. |
10/2/00
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7. | Medial triangle. The MEDIAL TRIANGLE is the triangle connecting the three midpoints of the sides. | Given 3 points, construct a triangle and it's medial triangle. |
10/2/00
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7a. | Orthocenter, Mid-segment triangle. | Given 3 points, construct the orthocenter. Next, construct the segments connecting each vertex to this orthocenter. Create the triangle formed by the midpoints of these segments. Name this triangle a Mid-segment triangle. |
12/12/00
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8. | Orthic triangle. The ORTHIC triangle is a triangle connecting the feet of the altitudes of a triangle. | Given 3 points, construct a triangle and its orthic triangle.. |
10/2/00
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9. | Pedal triangle. Let triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC (extended if necessary) locate three points R, S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P. | Given 3 points to define a triangle, and a 4th point to be any point on the plane, construct the pedal triangle. |
12/14/00
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10. | Center of Nine point circle. | Given 3 points, build a triangle and label the center of the Nine-Point circle (N). |
10/2/00
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11. | Nine Point Circle. | Given 3 points, build a triangle with it's Nine-Point circle. |
10/2/00
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12. | Trisecting a line segment. | Given two points, construct and trisect a segment. |
10/2/00
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13. | Equilateral triangle, given a side. | Given points AB, construct an equilateral triangle with side lengths AB. |
10/23/00
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14. | Square, given a side. | Given points AB, construct a square with side lengths AB. |
10/23/00
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15. | Isosceles triangle, given base and altitude. | Construct an isosceles triangle, given base and altitude. The script uses points A, B as the endpoints of the base, and points C, D as the endpoints of a segment defining the length of the altitude. |
10/23/00
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16. | Triangle Centers (H, G, C, and I). | Given 3 points, construct G, H, C, and I. |
9/25/00
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17. | Triangle Centers with Euler Line. | Given 3 points, construct the Euler line. |
9/25/00
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18. | Locus of vertex of a fixed angle that subtends a fixed segment. | ~~UNSOLVED~~ | |
19. | Divide a segment AB into two parts that form a golden ratio. | Given 2 points, divide a segment at the Golden Ratio. |
10/9/00
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20. | Pentagon, given a radius. | Given 2 points: center and vertex, construct a regular pentagon. |
10/9/00
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21. | Pentagon, given a side. | Given points AB, construct a regular pentagon with side lengths AB. |
10/23/00
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22. | Hexagon, given a side. | Given points AB, construct a regular hexagon with side lengths AB. |
10/23/00
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23. | Octagon, given a side. | Given points AB, construct a regular octagon with side lengths AB. |
10/23/00
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24. | Tangent lines to two circles. | Given rim, center and rim, center of two circles, construct all tangents to both circles |
10/16/00
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25. | Decagon, given a radius. | Given center and vertex, construct a regular 10-gon. |
10/9/00
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26. | Sublime triangle. | Given 2 points, construct a Sublime triangle. |
10/9/00
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27. | 2D cube | Given three points, construct a 2D representation of a cube. |
10/23/00
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28. | Circle tangent to two circles | Given two circles (actually, define 4 points as point-center, point-center of two circles), this script will construct a circle tangent to the other two. | 12/13/00 |
29. | Circle (2nd) tangent to two circles | Given two circles (actually, define 4 points as point-center, point-center of two circles), this script will construct a different circle tangent to the other two. | 12/13/00 |
30. | Two Circles tangent to two circles | Given two circles (actually, define 4 points as point-center, point-center of two circles), this script will construct two distinct circles tangent to the other two. | 12/13/00 |
31. | Two Circles tangent to two circles | Put 2 points to determine a line and then a point-center to determine a circle. This script will construct two circles tangent to the line and the circle. | 12/13/00 |
Comments? Questions? e-mail me at blawler@coe.uga.edu |
Last revised: December 28, 2000 |