Calculating the Segmented Helix
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  • Release Date: 27 Feb 2023
  • solid geometry
  • helix
  • Chasles’ theorem
  • platonic helix
Video Introduction

This video is adapted from 10.3390/math10142533

Eric Lord has observed: “In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant.” This video proves Lord’s observation. Constant-time algorithms are given for the segmented helix generated from the intrinsic properties of a stacked object and its conjoining rule. Standard results from screw theory and previous work are combined with corollaries of Lord’s observation to allow calculations of segmented helices from either transformation matrices or four known consecutive points. The construction of these from the intrinsic properties of the rule for conjoining repeated subunits of arbitrary shape is provided, allowing the complete parameters describing the unique segmented helix generated by arbitrary stackings to be easily calculated. Free/Libre open-source interactive software and a website which performs this computation for arbitrary prisms along with interactive 3D visualization is provided.

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Read, R.L. Calculating the Segmented Helix. Encyclopedia. Available online: (accessed on 02 March 2024).
Read RL. Calculating the Segmented Helix. Encyclopedia. Available at: Accessed March 02, 2024.
Read, Robert Lee. "Calculating the Segmented Helix" Encyclopedia, (accessed March 02, 2024).
Read, R.L. (2023, February 27). Calculating the Segmented Helix. In Encyclopedia.
Read, Robert Lee. "Calculating the Segmented Helix." Encyclopedia. Web. 27 February, 2023.