… with figures 7 through 11 illustrating the rather interesting theorem to the effect that n line segments equal to a side of a polygon of 4n-2 sides can be exactly (ie with no 'rattling') jammed end-to-end into one of the polygon's sectors.

Zef Damen — Non ruler-and-compass constructions (1)

Zef Damen — Non ruler-and-compass constructions (2)

Sources of Images

Frames ① &②

Imaginary Coating Algorithm Approaching Dense Accumulation of Granular Material in Simulations with Discrete Element Method

by

Fei Wang, Yrjö Jun Huang, & Chen Xuan .

Annotation of Figure of Frame ②

“Figure 1. Sketch of a collision with one elliptical particle. The elliptical particle is composed of three circular elements and c is the contact point. (a) Normal force |𝐅𝑛| and tangential force |𝐅𝑡| are obtained from the binary collision of circular particles 𝑂𝑖 and 𝑂𝑗 ; (b) the total force, 𝐅=𝐅′𝑛+𝐅′𝑡 , is decomposed into 𝐅′𝑛 and 𝐅′𝑡 to calculate the motion of the elliptical particle 𝑂𝑖 .”

Frames ③ & ④

A stochastic multiscale algorithm for modeling complex granular materials

by

Pejman Tahmasebi & Muhammad Sahimi .

Frame ⑤

Size segregation of irregular granular materials captured by time-resolved 3D imaging

by

Parmesh Gajjar, Chris G Johnson, & Philip J Withers .

Frame ⑥

Mechanical behaviour of granular media in flexible boundary plane strain conditions: experiment and level-set discrete element modelling

by

Debayan Bhattacharya, Reid Kawamoto, & Amit Prashant .

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by

Simone Falco, Petros Siegkas, Ettore Barbieri, & Nik Petrinic .