The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line

We explore the geometric properties of a conical frustum whose height extendsalong the entire positive real number line. Starting with a frustum of finite di-mensions (minor base diameter 1, major base diameter 10, height 1), we investigatewhat happens when the height parameter is allowed to grow without bound throughall positive real numbers. We demonstrate that this construction maintains its fun-damental geometric identity as a conical frustum while providing an intriguing ge-ometric interpretation of the real number line. This work establishes connectionsbetween elementary solid geometry, infinite structures, and the topological proper-ties of R+.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-01-02
DOI
https://doi.org/10.5281/zenodo.18131555
Primary Topic
Mathematics and Applications
Type
article
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article

The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line

10 MATH, Zen Revista
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
article

The Infinite Conical Frustum: A Geometric Embedding of the Real Number Line

10 MATH, Zen Revista
article en

Abstract

We explore the geometric properties of a conical frustum whose height extendsalong the entire positive real number line. Starting with a frustum of finite di-mensions (minor base diameter 1, major base diameter 10, height 1), we investigatewhat happens when the height parameter is allowed to grow without bound throughall positive real numbers. We demonstrate that this construction maintains its fun-damental geometric identity as a conical frustum while providing an intriguing ge-ometric interpretation of the real number line. This work establishes connectionsbetween elementary solid geometry, infinite structures, and the topological proper-ties of R+.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 95%
Mathematics and Applications
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