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神圣肘尺与谐振几何
古埃及肘尺、四分之一波长与双绞铜环的测量研究
The Sacred Cubit and Resonant Geometry: Measuring the Egyptian Royal Cubit, the Quarter Wave and the Bifilar Ring
DOI10.5281/zenodo.23666560摘要
古埃及皇家肘尺是一把约半米长、分为七掌二十八指的标准尺，今天又常被说成一种「神圣」的长度，并用作铜环与线圈的尺寸依据。本书不讨论肘尺是否神圣，而是提出五个可以测量的问题：现存肘尺有多长（都灵、卢浮宫、大英博物馆的馆藏记录为 52.3–52.5 厘米；本书以文献范围下限 523.5 毫米为工程常数）；按 λ = c/f，一肘尺与哪些声音和无线电波共振；双绞铜环在什么条件下抵消自身磁场（结论取决于股间是否绝缘、焊点如何连接），以及绞合收缩率如何决定下料长度；三个正交肘尺环构成的球面八面体中，场如何叠加、为何互不耦合；读者如何用 NanoVNA 与 RTL-SDR 在家中复现全部测量。
书中以标注框区分博物馆记录与已发表资料、可运行的 Python 推导与作者的假说；七个物件的测量方案事先写下预测，并承诺不论结果如何都原样公开原始数据。作者所在集团制作并销售肘尺铜环与张量线圈，书中已作利益披露；本书不作任何健康或医疗声明。
关键词：皇家肘尺；古埃及度量；都灵肘尺；四分之一波长共振；双线并绕；双绞线；驻波比；矢量网络分析仪
Abstract
The royal cubit of ancient Egypt was a standard ruler about half a metre long, divided into seven palms and twenty-eight fingers. Today it is often called a "sacred" length and used to size copper rings and coils. This book does not ask whether the cubit is sacred. It asks five measurable questions: how long the surviving rods are (museum records in Turin, Paris and London give 52.3–52.5 cm; the book uses 523.5 mm, the lower bound of the published range, as an engineering constant); which sounds and radio waves a cubit resonates with, using λ = c/f; when a twisted copper ring cancels its own magnetic field (it depends on whether the strands are insulated and how the joint is made), and how the twist contraction factor sets the cut length; how fields add in a spherical octahedron of three orthogonal cubit rings, and why such rings do not couple; and how readers can repeat every measurement at home with a NanoVNA and an RTL-SDR receiver.
Marked boxes separate museum records and published sources, runnable Python calculations and the author's hypotheses. A measurement plan for seven objects states its predictions in advance, and the raw data will be published unaltered whatever the results. The author's group makes and sells cubit rings and tensor coils, as disclosed in the book; the book makes no health or medical claims.
Keywords: royal cubit; Egyptian metrology; cubit rod; quarter-wave resonator; twisted pair; bifilar winding; standing-wave ratio; NanoVNA
目录 · Contents
- 序：一把尺子，五个可以测量的问题English 中文Preface: One Ruler, Five Measurable Questions
- 第一章 皇家肘尺有多长？English 中文Chapter 1. How Long Is a Royal Cubit?
- 第二章 一肘尺的波长：$\lambda = c/f$English 中文Chapter 2. The Wavelength of a Cubit: $\lambda = c/f$
- 第三章 双绞铜环：磁通抵消与驻波比English 中文Chapter 3. The Twisted Copper Ring: Flux Cancellation and SWR
- 第四章 多环正交几何：球面八面体与场的叠加English 中文Chapter 4. Multi-Ring Orthogonal Geometry: The Spherical Octahedron and the Superposition of Fields
- 第五章 开源硬件复现指南：用 NanoVNA 与 RTL-SDR 建立家庭射频测量台English 中文Chapter 5. An Open-Hardware Replication Guide: A Home RF Bench with NanoVNA and RTL-SDR
How to cite · 引用
Fan, Y. (2026). The Sacred Cubit and Resonant Geometry: Measuring the Egyptian Royal Cubit, the Quarter Wave and the Bifilar Ring [神圣肘尺与谐振几何] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23666560
BibTeX
@book{fan2026sacred,
title = {{The Sacred Cubit and Resonant Geometry}: Measuring the Egyptian Royal Cubit, the Quarter Wave and the Bifilar Ring},
author = {Fan, Yafu},
year = {2026},
publisher = {5D Library},
edition = {Version 1.0.0},
doi = {10.5281/zenodo.23666560},
url = {https://doi.org/10.5281/zenodo.23666560},
note = {Chinese title: 神圣肘尺与谐振几何}
}
| DOI | https://doi.org/10.5281/zenodo.23666560 |
|---|---|
| DOI（全部版本 all versions） | https://doi.org/10.5281/zenodo.23666559 |
| ORCID | https://orcid.org/0009-0004-3519-1203 |
| 5D Library ID | 5DL-B-003 |
| 版本 Version | 1.0.0 · 中英双语版 Bilingual edition |
| 出版日期 Date | 2026-10-26 |
| 网址 Online | https://5dlibrary.com/books/sacred-cubit-geometry/ |
| SHA-256 · sacred-cubit-geometry_bilingual_v1.0.0.pdf | 2b882fbd734d6c41f23f00cffd0e9f4039ca33cda04a844358da289efbcf58e4 |
| SHA-256 · sacred-cubit-geometry_en_v1.0.0.pdf | 9fe88242e3bc71485a40e47b100d2991130a492d2a314d8e2f4c518b2c7676fd |
| SHA-256 · sacred-cubit-geometry_zh_v1.0.0.pdf | 9d97d95a390616ebc29b80895fa6f8a1cb46de6a35f9d32f3b1babe251f0aa44 |
| Licence · 许可 | Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Disclosure. The author and the group that includes 5D Library run sacredcubit.com and tensorcoil.com, which make and sell hand-calibrated copper rings and tensor coils cut to the royal cubit of 523.5 mm. Because of this commercial interest, every measurement plan in the book states its predictions in advance and the raw data will be published unaltered; the book makes no health or medical claims.