# algebraic geometry

Published articles for algebraic geometry.

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## Elliptic Curves as Elementary Equations

DevFeed: [Elliptic Curves as Elementary Equations](<https://devfeed.tech/articles/elliptic-curves-as-elementary-equations-40343.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/02/10/elliptic-curves-as-elementary-equations/>)

Published: 2014-02-10T10:00:40Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [Security](<https://devfeed.tech/topics/security.md>)

Tags: [algebra](<https://devfeed.tech/tags/algebra.md>), [algebraic-geometry](<https://devfeed.tech/tags/algebraic-geometry.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [elliptic-curves](<https://devfeed.tech/tags/elliptic-curves.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [function](<https://devfeed.tech/tags/function.md>), [mathematica](<https://devfeed.tech/tags/mathematica.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [security](<https://devfeed.tech/tags/security.md>), [systems](<https://devfeed.tech/tags/systems.md>)

### AI overview

This introductory tutorial explains elliptic curves as the sets of solutions to cubic polynomial equations in two variables. It motivates their study through algebraic geometry and their role in encryption, then begins developing the elliptic curve group structure using an elementary example involving pyramids of spheres.

### Source excerpt

Finding solutions to systems of polynomial equations is one of the oldest and deepest problems in all of mathematics. This is broadly the domain of algebraic geometry, and mathematicians wield some of the most sophisticated and abstract tools available to attack these problems. The elliptic curve straddles the elementary and advanced mathematical worlds in an interesting way. On one hand, it's easy to describe in elementary terms: it's the set of solutions to a cubic function of two variables.