Poet's Corner

Explanation: "Geometry"

In this first line, Dove sets the stage for the rest of the poem. The speaker asserts indisputable rational knowledge ("I prove a theorem") and immediately a mysterious force is set in motion ("the house expands").
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Lines 2-3

In these lines, inanimate objects, which are the product of rational thinking, take on living and even human characteristics: "the windows jerk free to hover near the ceiling," and "the ceiling floats away with a sigh." This attribution of human characteristics to inanimate objects is known as personification.
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Lines 4-6

In these lines, the mysterious force that dismantles everything that is known and certain continues. The walls disappear, "the scent of carnations leaves with them," and suddenly the speaker is no longer protected: "I am out in the open." The use of carnations may suggest a celebration of moving from one level of knowledge to another.
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Lines 7-9

In the final tercet, the transformation is complete: "above the windows have hinged into butterflies." Windows, rationally constructed frames of perception, have been transformed into living creatures of the imaginative realm, "sunlight glinting where they've intersected." The poet seems to be suggesting that where rational thought and imagination intersect there is enlightenment. These imaginatively transformed creatures "are going to some point true and unproven."
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Source: Exploring Poetry, Gale, 1997.