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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.
The "nine dots" puzzle (left) has the goal of linking all 9 dots using four straight lines or less, without lifting the pen. Its solution (right) is to draw those lines "outside the box". Since at least 1954, the nine dots puzzle has been used as a metaphor of the type "think beyond the boundary".
The emergence of connect the dots games in the printed press takes place in the early 20th century. These games were published with other puzzle games as pastime for children on the Sunday edition. While the first books containing connect the dots games exclusively were printed in 1926 by Ward, Lock & Co. [4] A mostly complete puzzle
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Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively. A point on a line gives a combination of 2p and 5p for its given total (green). Multiple points on a line imply multiple possible combinations (blue). Only lines with n = 1 or 3 have no points (red).
Blind contour drawing is a drawing exercise, where an artist draws the contour of a subject without looking at the paper. The artistic technique was introduced by Kimon Nicolaïdes in The Natural Way to Draw, and it is further popularized by Betty Edwards as "pure contour drawing" in The New Drawing on the Right Side of the Brain.
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A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4. The center N of the nine-point circle bisects a segment from the orthocenter H to the circumcenter O (making the orthocenter a center of dilation to both circles): [6]: p.152