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Take any triangle and divide it into sub-triangles as shown. Inscribe a circle in each of these smaller triangles.

Rearrange the order of the circles and adjust the intervening lines so that each line touches two circles:

No matter how this is done, each circle will always fit perfectly in its triangle.


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This photo was taken at the reopening of the South Fork Bridge in Gold Bridge, British Columbia, in 1941. It’s sometimes claimed that the man at the center appears too modern to belong in such a crowd. It’s true that he’s dressed more casually than those around him, but the sunglasses he’s wearing first appeared in the 1920s, and his “T-shirt” appears to be a sweater ...


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Update

Catullus wrote this poem in the first century B.C.:

Mourn, o Venuses and Cupids
and however many there are of more charming people:
my girl’s sparrow is dead—
the sparrow, delight of my girl,
whom that girl loved more than her own eyes.
For he was honey-sweet and had known
the lady as well as a girl [knows] her mother herself,
nor did he mov...


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Image: Wikimedia Commons

Each of these buses is proceeding smoothly along the striped street. Yet each seems to be varying its speed dramatically.

When the blue bus encounters a white stripe, it becomes easy to see due to the high contrast...


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What does this say? It’s an excerpt from a small bound volume given in 1841 by Harvard law professor Theophilus Parsons Jr. to John Davis of the Massachusetts Historical Society. Davis noted, “It was found in his father’...


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