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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 or retracing any lines.
: origin of the line : distance from the origin of the line : direction of line (a non-zero vector) Searching for points that are on the line and on the sphere means combining the equations and solving for , involving the dot product of vectors:
Given a line and any point A on it, we may consider A as decomposing this line into two parts. Each such part is called a ray and the point A is called its initial point. It is also known as half-line (sometimes, a half-axis if it plays a distinct role, e.g., as part of a coordinate axis). It is a one-dimensional half-space. The point A is ...
In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf together with a linear functional : (,) that induces a natural isomorphism of vector spaces
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
An isoporic line refers to a line of constant annual variation of magnetic declination . [33] An isoclinic line connects points of equal magnetic dip, and an aclinic line is the isoclinic line of magnetic dip zero. An isodynamic line (from δύναμις or dynamis meaning 'power') connects points with the same intensity of magnetic force.
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
One of the most fundamental elements of art is the line. An important feature of a line is that it indicates the edge of a two-dimensional (flat) shape or a three-dimensional form. A shape can be indicated by means of an outline, and a three-dimensional form can be indicated by contour lines. [1]
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