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Some lines in the pencil through A. In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane.
It has gone by many other names, [2] including dots and dashes, game of dots, [3] dot to dot grid, [4] boxes, [5] and pigs in a pen. [6] The game starts with an empty grid of dots. Usually two players take turns adding a single horizontal or vertical line between two unjoined adjacent dots.
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
Drafting pantograph in use Pantograph used for scaling a picture. The red shape is traced and enlarged. Pantograph 3d rendering. A pantograph (from Greek παντ- 'all, every' and γραφ- 'to write', from their original use for copying writing) is a mechanical linkage connected in a manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical ...
Sprouts is an impartial paper-and-pencil game which can be analyzed for its mathematical properties. It was invented by mathematicians John Horton Conway and Michael S. Paterson [1] at Cambridge University in the early 1960s.
Turtle graphics are often associated with the Logo programming language. [2] Seymour Papert added support for turtle graphics to Logo in the late 1960s to support his version of the turtle robot, a simple robot controlled from the user's workstation that is designed to carry out the drawing functions assigned to it using a small retractable pen set into or attached to the robot's body.
Many pen movement recording systems capture, not only the x and y coordinates of the pen top, but also axial pen pressure, an x an y tilt or altitude and azimuth of the pen barrel. Handwriting movement measurement systems can capture: x = Horizontal coordinates; parallel to the baseline in Western script
In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms, now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry).
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