Questions tagged [geometry]
A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, the relative position of figures, and the properties of space. Use with [mathematics]
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Prove/disprove that polygons on a sheet of paper having a common edge, can always be colored with one of two different colors.
Several straight lines drawn on a sheet of paper divide it into polygons. Is it always possible to color each polygon with one of two colors so that any two polygons that share an edge are of ...
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Where should the bridges be built to minimize the length of the path between two towns?
Two towns are separated by two rivers, as in the diagram.
The banks of each river are parallel lines. Where should bridges that cross the river perpendicular to the banks be built so that the distance ...
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Can a 10*10 square be paved with 1*4 rectangular stone plates?
Can a 10 * 10 square be paved with 1*4 rectangular stone plates?
I seek a very intuitive and simple answer to this puzzle.
P.S. Will post the source later. The source contains the answer but it is not ...
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Crossing a square pond with beams
Here is a classical mathematical puzzle:
In the middle of a square pond lies a square island (whose sides are aligned with the sides of the pond). On the island is a tower with a princess locked ...
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Regular pentagram inscribed in a parabola
The diagram shows a regular pentagram inscribed in a parabola.
Can another red pentagon (congruent to the one shown) fit in the gray region?
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Three-cushion billiards challenge.
World champion three-cushion billiards player can perfectly make a billiard ball end where asked for (if possible), on a standard rectangular shaped competition table.
The champion now, for ...
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A "crappy" pentagon puzzle
Lately, we've had plenty of puzzles based on the regular pentagon and its geometric properties. So I propose one that literally brings it all together.
Use eleven copies of the larger (left) piece ...
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Sliding coins down an envelope
The envelope is a regular pentagon with two diagonals. The red coins are two vertically aligned and touching congruent circles, the top one passing through the apex of the pentagon, and the bottom ...
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Two semicircles in a parallelogram
Two congruent semicircles (blue) are inscribed in the two triangles formed by the short diagonal (black) of a parallelogram (also black) as shown below. The short diagonal has the same length as the ...
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Heptagons trompe-l'œil ?
Seven outer blue, equal sized, regular heptagons touch the sides of a given, also equal sized, inner blue regular heptagon.
The green triangle has black vertices: the south and the, up to one, most ...
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A single magical ant wandering in a vast garden of cubes
The following image depicts a small part of a vast "cube garden":
This garden started as a single 1x1x1 cube, which was grown into the complex shape you see here by performing the following ...
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Can another circle fit in this diagram?
Two vertically-aligned and touching congruent (blue) circles are inscribed in a pendant (the black quadrilateral) in a regular star as shown below. Can you fit another circle of the same size that’s ...
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Circles in a pendant in a star
Four vertically-aligned touching circles of equal radius are inscribed in a pendant (the black quadrilateral) inside a regular star as shown in the figure below. Show that the centre of the green ...
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Two semicircles in a regular pentagon
Two semicircles, pink and blue, are inscribed inside a regular pentagon as shown in the figure. Which semicircle is bigger?
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Two triangles in a light bulb
Here’s a light bulb made of a regular dodecagon (yellow), two equilateral triangles (light gray), and a square (dark gray). Show that the red and blue triangles have the same area.
Of course, you can ...
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