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Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...
The computer could control in 0.01 inches (0.25 mm) increments the rotation of an 11-inch (280 mm) wide drum, and the horizontal movement of a pen holder over the drum. The pen was pressed by a spring against paper scrolling across the drum. A solenoid could lift the pen off the paper. This arrangement allowed line drawings to be made under ...
Text (produced by an ISO stencil template for use with the technical pens) of 5 mm in height has a stroke or line thickness of 0.5 mm, and so requires a brown-nibbed 0.5 mm pen. If this text were used in an ISO-sized document (e.g. A0), and the document were reproduced at half its original height (A2), the text would be rendered 2.5 mm high ...
The pen's dimensions are 5 + 7 ⁄ 8 by 1 ⁄ 2 inch (14.9 cm × 1.3 cm) with the cap, [11] or 14.5 cm × 0.7 cm (5 + 11 ⁄ 16 in × 1 ⁄ 4 in) without the cap. The Cristal's design has been widely copied around the world, especially in the Far East.
For solving the cubic equation x 3 + m 2 x = n where n > 0, Omar Khayyám constructed the parabola y = x 2 /m, the circle that has as a diameter the line segment [0, n/m 2] on the positive x-axis, and a vertical line through the point where the circle and the parabola intersect above the x-axis.
The mapping from 3D to 2D coordinates is (x′, y′) = ( x / w , y / w ). We can convert 2D points to homogeneous coordinates by defining them as (x, y, 1). Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0.
A plot of () (left) and its phase line (right). In this case, a and c are both sinks and b is a source. In mathematics , a phase line is a diagram that shows the qualitative behaviour of an autonomous ordinary differential equation in a single variable, d y d x = f ( y ) {\displaystyle {\tfrac {dy}{dx}}=f(y)} .