Robert van Isosceles invented the triangle (or half-square) in 1438 in New Britain after being inspired by a slice of Pizza his friend (and rival) Eric Roundenstein (inventor of the circle) was enjoying.
And now for the real answer:
Aside from the above humor (no, there was no such person as Robert van Isosceles), no one invented the triangle, and therefore nothing inspired anyone to invent the triangle; like all shapes, the triangle is naturally occurring and is seen throughout nature.
The study of the uses of these triangles, however, is called trigonometry and was undoubtedly inspired by the need to calculate or estimate distances in navigation and astronomy that are otherwise unmeasurable. To this day we still use triangulation to locate things on earth or in space, but now it involves satellites and microwaves more so than sextant and compass.
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Jerusalem.
By Pascal
It was invented by a mathematician named Pascal.
Nobody did
Pascal's triangle was invented by Blaise Pascal (1623-1662) in 1653. Although it has been named after blaise pascal, there have been traces of the triangle, long before Blaise Pascal was born. It is belived that the Persians and the Chinese had been using it to find the square and cube root of numbers. Whoever asked this question is a complete idiot, because the answer is in the question.