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In 2020, researchers Joshua Greene and Andrew Lobb made significant strides in the smooth curves case, demonstrating that within this narrower field, rectangles of any aspect ratio can be inscribed. The distinction of smoothness plays a fundamental role in the proof’s cleanliness, emphasizing the need for continuous behavior when tracing angles and distances.

The Underlying Nature of Topology

Ultimately, the exploration of topology stretches far beyond illogical shapes. Understanding the interplay of continuous associations between dots on a closed curve is the essence of the discipline. The quest for logical clarity in topology often uncovers profound insights, revealing connections between dimensions and challenges that dazzle and perplex mathematicians.