Óvalo dados sus dos ejes

Óvalo dados sus dos ejes


We are going to draw an oval given the length of its two axis, which can be seen at the top of the screen. Line segment “AB” and “CD”. The first step we are going to do is to situate this two axis. So to start we will draw a horizontal straight line in the middle of our screen, and mark a point “A” on the left side of this line, as can be seen here. Now we are going to transport our larger axis “AB” onto our horizontal line. Setting our compass to the length of axis “AB” we will now transport it onto our horizontal line, setting our compass on “A” and scribing point “B” on the horizontal line. So now that we have the horizontal axis “AB” we are going to work out its perpendicular bisector because this is where our second smaller axis “CD” will be located. To draw this perpendicular bisector, firstly we must draw two arcs which are centered on both ends of our axis “AB”, as can be seen in the video. These arcs are going to have the same radius, the only condition is that the lengths of the radius must be longer than half the length of the axis “AB”. These arcs intersect at two points which we will join to obtain our perpendicular bisector. This perpendicular bisector cuts the axis “AB” at a point which we will call “0”. So the next step is to work out the perpendicular bisector of the smaller axis “CD” so as to work out its midpoint. As the smaller axis “CD” is located on the top of our screen we are going to use a different method to work out its perpendicular bisector because we don’t have enough space to use our previous method. We are going to draw four arcs, with two different radiuses, one radius for the first two arcs and a slightly shorter radius for the second two arcs. The first two radiuses will intersect each other at a point while the second two radiuses will intersect each other at a different point. So now we join these two points with a line and this line will be the perpendicular bisector. This perpendicular bisector cuts the axis “CD” in half at the midpoint “M”. Using our compass, set on point “M” to point “D” we will transport this length on to the vertical bisector, above and below the midpoint “O”, as can be seen here in the video. Now I have the two axises of our oval located correctly. Next step is, with our compass centered on “O”, with a radius “OA” we will scribe an arc to the right until it cuts the vertical bisector and we will call this point “A1”. So now we join point “A” to point “C”. Now, with our compass centered on “C” with a radius “C-A1” we are going to scribe an arc to the left until it cuts our previously drawn line “AC” at a point we will call “A2”. The next step is to calculate the perpendicular bisector of the line-segment “A-A2”. To do this we use the first method drawing two intersecting arcs above and below the line segment “A-A2”, as can be seen in the video. We try to keep these arcs as small as possible so as not to clutter the drawing. So now we draw the perpendicular bisector which will intersect our two axis at points O1 and O2 as can be seen here in the video. These points will be two centers of our oval. So now we must obtain the mirror images of these two points. To do this, with the compass set on the origin “O” and with radius “O-O1” we scribe an arc to the right to cuts our horizontal axis “AB”. Now with our compass set on the origin “O” and radius “O-O2” we scribe an arc to the left until we cut our vertical axis “CD”. These two new points we will call “O3” and “O4” as can be seen here in the video. So now we are going to join point “O2” to point “O3” and we will prolongate this line as can be seen in the video. We will repeat this process by joining points “O4” to “O1” and prolongating this line also as can be seen here in the video. And finally we join points “O4” to “O3” again prolongating this line as can be seen in the video. So the last step is to draw the four arcs that make up our oval. With compass centered on point “O1” and radius “O1-A” we will draw the left side of our oval as can be seen here in the video from until it cuts our previously drawn prolongations. As you can see I’m going to use a thicker line to draw these arcs. So now, with the compass centered on point O3, and the same radius “O1-A” we will draw another arc which will be the right side of our oval as can be seen here in the video. So the next step we will draw the third arc, with our compass centered on point “O2”. And finally, with our compass centered on point “O4”, we will finish drawing our oval. Here you have the oval made up of four independent arcs with four independent centre points. The contact points of these arcs are aligned with their centers and because of that there are tangent points. We will assign the letter “T” for tangent point to these four points.