One such poet is Baba Taher. I visited his mausoleum on my trip to Hamedan a couple of years ago. He was an 11th century mystic who became a poet almost by accident. It is said that he was a naive, innocent child who people often made fun of. One winter day, some people challenged him to swim in the fountain, telling him that if he did, he'd become a poet. He swam in the fountain, and much to the chagrin of the pranksters, a poet was indeed born.
The mausoleum is set in a beautiful park with winding pathways all around. It's an octagonal shape, and inside, the walls have marble slaps with his poetry etched into them. (One of his poems was featured here at My Persian Corner as part of Poetry Sunday.) To make the visit complete, I was lucky enough to hear some of his poetry by a local man who had happened to come pay his respects to this esteemed poet. He had a voice that was created for reciting poetry, and the structure provided the best acoustics.
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If you visit Hamedan, this is definitely one of the must-see sites!