Two White Blocks: Why Fig. 17 and Fig. 171 Were Never Really Assembled
Year: 2026
Type: preprint
Abstract: Two White Blocks: Why Fig. 17 and Fig. 171 Were Never Really Assembled This paper proves that Fig. 17 and Fig. 171 in Freese's collection are not successful dissections, but drawn dissections. Area equality wh = s^2 guarantees only equal area, not congruent pieces. Fig. 17 attempts a cut of 2 green + 2 blue strips but leaves a white hole in B. The two remaining small white blocks do not match: M white width = 0.793, B white width = 2.249, difference = 1.456. Fig. 171 does not even attempt a cut — it shows only two white frames, M white a x b, ABCD, and B white s x s, EFGH. The cut line in M should be sqrt(a^2 + (b-a)^2) = 1.211, not s = 1.166, difference = 0.045. The P-template cannot cut M and B at the same time, because its base, height and side cannot satisfy all three equations at once. This is the first measurement-based verification that measures the figures all the way down to the cut line. Author: Brett LinCorrespondence: via Zenodo recordKeywords: dissection, Fig. 17, Fig. 171, P-template, Freese
Author: Lin, Xu Brett
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225759885
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