To do this, press the add point button, and click anywhere on the line. A Line object shares all properties from a Draft Wire , however, only some of these properties are applicable to the Line.
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The Line tool can be used in macros and from the Python console by using the following function:. Jump to: navigation , search.
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Other languages:. Next: Wire. Navigation menu Personal tools English Log in. Namespaces Page Discussion. If two coplanar circles, the diameter of one of which is equal to half the diameter of the other, are taken to be internally tangent at a point, and if a point is taken on the smaller circle—and let it be at the point of tangency—and if the two circles move with simple motions in opposite direction in such a way that the motion of the smaller is twice that of the larger so the smaller completes two rotations for each rotation of the larger, then that point will be seen to move on the diameter of the larger circle that initially passes through the point of tangency, oscillating between the endpoints.
I don't quite understand why he was interested in this, but it has something to do with using epicycles to build linear motion out of circular motion. It also has something to do with the apparent motion of planets between the Earth and the Sun. Later Copernicus also studied the Tusi couple.
He proved that the moving point really did trace out a straight line:. However, many suspect that this was not a true rediscovery: al-Tusi had also proved this, and some aspects of Copernicus' proof seem too similar to al-Tusi's to be coincidence:. In fact, the Tusi couple goes back way before al-Tusi.
It was known to Proclus back around AD! Apparently he wrote about it in his Commentary on the First Book of Euclid. Proclus is mainly famous as a philosopher: people think of him as bringing neo-Platonism to its most refined heights. Given that, it's no surprise that he also liked math.
Indeed, he said:. So, here are three proofs that a Tusi couple really does trace out a straight line. I like them because they're very different.
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Since people have thought about Tusi couples since AD, I doubt any of these proofs are original to the people I'm mentioning here! Still, they deserve credit. Let O be the center of the big circle. Let A be the position of the traced point at the instant t when it's the point of tangency between the circles, let B be its position at some future time t. Let X be the center of the small circle at that future time t.. We want to prove A, B and O lie on a line.
The arc AC of the big circle has the same length as the arc BC of the small circle, since they are both the distance rolled between times t and t.. The second proof is due to Greg Egan.
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He distilled it down to a moving picture:. It's a 'proof without words', so you may need to think a while to see how it shows that the Tusi couple traces out a straight line. The third proof is due to Boris Borcic. It uses complex numbers. Let the big circle be the unit circle in the complex plane.
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Then the point of contact between the rolling circle and the big one is:. Since the rolling circle turns around once clockwise as it rolls around the big one, the point whose motion we're tracking here:. But the same sort of argument shows that if we track the motion of the opposite point on the rolling circle, it equals:. So, this opposite point moves back and forth along a horizontal straight line So, the rectangle here illustrates the fact that.
When the ball is below it another rule applies. It is also used as a reference for offensive player alignment.
Top Of Circle Key The top of circle is the area straight out from the basket just outside the free throw circle. The wing on the same side as the ball handler is the "Ballside or Strongside" wing. Corner The "Corner" is primarily used to designate the area where the sideline and baseline meet. This is another favorite area from which players like to shoot. It is usually an open area when zone defense is played. However, it is also an area where the defense can readily trap an offensive player with the ball. Short Corner The short corner is an area along the baseline half way between the sideline and the lane line.
It is a strategic offensive area especially used against zone defenses. No offensive charges can be taken by defenders when they are positioned on or inside this area. How HoopTactics Works. Explore The Free Area. Sign Up For Premium Membership. Basketball Basics. Basketball Court Areas. Player Positions. Types Of Basketball Offenses. Offensive Player Skills. Types of Basketball Defenses. Person-To-Person Defenses. Zone Defenses. Combination Defenses.
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