Separating Visual Perspective from Earth's Curvature: A Geometric Study of the Apparent Horizon
Abstract
Research Title: Separating Visual Perspective from Earth's Curvature: A Geometric Study of the Apparent Horizon
Author: Sami Ullah
Abstract
This preliminary theoretical study investigates the relationship between Earth's curvature, visual perspective, and the apparent horizon. The research originated from a personal observation made in 2024 concerning why distant objects appear progressively smaller and why the ground seems to meet the sky at the horizon.
The manuscript examines these observations using established principles of geometric optics, angular size, spherical geometry, and line-of-sight tangency. It distinguishes the reduction in apparent object size caused by perspective from the geometric limitations on visibility caused by Earth's curvature.
Mathematical relationships are used to illustrate how observer height affects geometric horizon distance and how an object's angular size changes with distance. The study also propose
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BibTeX
@misc{ullah2026separating,
title = {{Separating Visual Perspective from Earth's Curvature: A Geometric Study of the Apparent Horizon}},
author = {Sami Ullah},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23614707},
url = {https://zenodo.org/records/23614707},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Separating Visual Perspective from Earth's Curvature: A Geometric Study of the Apparent Horizon
AU - Sami Ullah
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23614707
UR - https://zenodo.org/records/23614707
AB - Research Title: Separating Visual Perspective from Earth's Curvature: A Geometric Study of the Apparent Horizon Author: Sami Ullah Abstract This preliminary theoretical study investigates the relationship between Earth's curvature, visual perspective, and the apparent horizon. The research originated from a personal observation made in 2024 concerning why distant objects appear progressively smaller and why the ground seems to meet the sky at the horizon. The manuscript examines these observations using established principles of geometric optics, angular size, spherical geometry, and line-of-sight tangency. It distinguishes the reduction in apparent object size caused by perspective from the geometric limitations on visibility caused by Earth's curvature. Mathematical relationships are used to illustrate how observer height affects geometric horizon distance and how an object's angular size changes with distance. The study also propose
ER -