planimeter वाक्य
उदाहरण वाक्य
मोबाइल
- The images show the principles of a linear and a polar planimeter.
- A planimeter is a device which does integrals, using distance as the analog quantity.
- The polar planimeter is restricted by design to measuring areas within limits determined by its size and geometry.
- In 1893 Durand published a paper mathematically describing a radial planimeter for averaging values plotted in polar coordinates.
- The pointer M at one end of the planimeter follows the contour C of the surface S to be measured.
- When the planimeter's measuring wheel moves perpendicular to its axis, it rolls, and this movement is recorded.
- The working of the linear planimeter may be explained by measuring the area of a rectangle ABCD ( see image ).
- The same figure was also used in the old town plan of Quezon and was validated by using a digital planimeter.
- Originally a radial planimeter was of academic interest only, but ten years later clock driven recording instruments started being used.
- In 1887 Petersen had constructed another model; a planimeter which was presented to the Royal Danish Academy of Science and Letters.
- For the polar planimeter the " elbow " is connected to an arm with its other endpoint O at a fixed position.
- For the linear planimeter the movement of the " elbow " E is restricted to the " y "-axis.
- That means the planimeter measures the distance that its measuring wheel travels, projected perpendicularly to the measuring wheel's axis of rotation.
- That November, while attending a conference on computer graphics in Reno, Nevada, Engelbart began to ponder how to adapt the underlying principles of the planimeter to X-Y coordinate input.
- A direct development of the planimeter known as an integraph, or integerometer, can be used to establish the position of the centroid or center of mass of an irregular two-dimensional shape.
- I attacked her with proportional dividers, planimeter, rotameter, Simpson's rule, Froude's coefficients, Dixon Kemp's formulae, series, curves, differentials, and all the appliances of modern yacht designing, and she emerged from the ordeal a theoretically perfect boat.
- A mechanical device that computes area integrals is the planimeter, which measures the area of plane figures by tracing them out : this replicates integration in polar coordinates by adding a joint so that the 2-element linkage effects Green's theorem, converting the quadratic polar integral to a linear integral.
- Green's Theorem, which gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C, is applied in an instrument known as a planimeter, which is used to calculate the area of a flat surface on a drawing.
- For a polar planimeter the total rotation of the wheel is proportional to \ scriptstyle \ int _ t r ( t ) \, \ dot \ theta ( t ) \, dt, as the rotation is proportional to the distance traveled, which at any point in time is proportional to radius and to change in angle, as in the circumference of a circle ( \ scriptstyle \ int r \, d \ theta = 2 \ pi r ).
- This last integrand \ scriptstyle r ( t ) \, \ dot \ theta ( t ) can be recognized as the derivative of the earlier integrand \ scriptstyle \ tfrac { 1 } { 2 } ( r ( t ) ) ^ 2 \ dot \ theta ( t ) ( with respect to " r " ), and shows that a polar planimeter computes the area integral in terms of the " derivative ", which is reflected in Green's theorem, which equates a line integral of a function on a ( 1-dimensional ) contour to the ( 2-dimensional ) integral of the derivative.
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