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If parallel lines could meet: What exactly can a poet say about the Fano plane?

This article describes our invention of a new poetic form based on projective geometry. In doing this we also explore the 'what ifs' in mathematics and poetry which spark the creative processes of poet and mathematician. In other words, throughout our collaboration we often asked one another, is this what it's like for you? Do you think in this way, too? How does your experience of creativity compare to mine? And often, as well, what exactly do you mean when you say...? We spent a fair amount of time and energy, for example, trying to understand one another's interpretation of 'a line'. This collaboration resulted in three poems in the new projective plane form. We also consider what might be interesting avenues for future research, such as the incorporation of octonions in poetic form.