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Geometrical Quotes

Precise language for shape, structure, and scale.

These geometrical quotes draw from mathematics, chemistry, and population theory alike — from decomposing planar figures into triangles, to the molecular geometry Behind chemical reactions, to population growth famously described as geometrical.

A planar geometrical figure with more than three vertices can be decomposed into a set of triangles, and it can be reconstructed from a set of triangles.

Quotes by Vladimir Prelog

Population, when unchecked, increases in a geometrical ratio.

Quotes by Thomas Malthus

Population, when unchecked, goes on doubling itself every 25 years or increases in a geometrical ratio.

Quotes by Thomas Malthus

General relativity is the cornerstone of cosmology and astrophysics. It has also provided the conceptual basis for string theory and other attempts to unify all the forces of nature in terms of geometrical structures.

Quotes by Paul Davies

Able Quotes

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.

Quotes by Martin Gardner

This simple idea served to provide information on the geometrical shape of reacting molecules, and I was able to make the role of the frontier orbitals in chemical reactions more distinct through visualization, by drawing their diagrams.

Quotes by Kenichi Fukui

For polyatomic free radicals and ions, one is dependent both for the ground states and the excited states on the study of electronic spectra to obtain the shapes and the geometrical parameters.

Quotes by Gerhard Herzberg

The concentration and reciprocal effect of industry and agriculture conjoin in a growth of productive powers, which increases more in geometrical than in arithmetical proportion.

Quotes by Friedrich List

It is impossible to anticipate all of the misdeeds engendered by the universal conflict of human passions. They multiply at a compound rate with the growth in population and the interlacing of particular interests that cannot be directed with geometrical...

Quotes by Cesare Beccaria

Frequently Asked Questions

What mathematical idea does the first geometrical quote describe?
It describes how any planar figure with more than three vertices can be broken down into a set of triangles, and reconstructed from that same set — a foundational idea in geometry.
How does geometry connect to chemistry in these quotes?
One quote explains that understanding the geometrical shape of reacting molecules helped clarify the role of frontier orbitals in Chemical Reactions, linking shape directly to reactivity.
What does 'increases in a geometrical ratio' mean regarding population?
It means population grows multiplicatively rather than by fixed amounts — two quotes here both state that unchecked population doubles roughly every 25 years, growing geometrically rather than steadily.
Why are there two very similar population quotes in this set?
They restate the same core idea from slightly different angles — one adds the specific 25-year doubling detail, while the other states the geometrical ratio more simply.
Do these geometrical quotes stay purely theoretical?
No — they connect abstract geometric principles to real applications in chemistry and demography, showing how the same mathematical idea explains very different phenomena. See our Able quotes for more on applied reasoning.

Two nearly identical lines both warn that unchecked population increases in a geometrical, not simple, ratio. For related scientific reasoning, see our Chemical Reactions quotes.