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The 20 pages that link to Transcendental number, each with the reason it gives.

• Rational numberCompared with: No rational number is transcendental.

• Algebraic numberCompared with: It is precisely the alternative to being algebraic.

• Irrational numberBroader topic: Every transcendental number is irrational, though some irrational numbers are algebraic.

• PiBroader topic: Pi is transcendental, a stronger property than irrationality.

• Root of unityCompared with: Every root of unity is algebraic, making transcendental numbers a sharp contrast.

• Lindemann–Weierstrass theoremNarrower topic: The theorem establishes transcendence by ruling out algebraic relations involving exponentials.

• Joseph LiouvilleRelated: His construction gave the first explicit examples of numbers beyond the algebraic numbers.

• Squaring the circleNarrower topic: A transcendental π cannot be a constructible length.

• Charles HermiteNarrower topic: Hermite established that e belongs to this class, a landmark result in number theory.

• Constructible numberCompared with: No transcendental number can be constructible, since construction steps yield algebraic numbers.

• Straightedge and compass constructionRelated: Pi's transcendence proves that a circle's area cannot be matched by a constructible square.

• Algebraic integerCompared with: It lies outside the algebraic numbers, and therefore outside the algebraic integers.

• Dirichlet's approximation theoremNarrower topic: The theorem applies to transcendental numbers too, while stronger approximation can help establish transcendence.

• Transcendence theoryBroader topic: These are the objects the theory aims to identify and compare.

• Euler–Mascheroni constantCompared with: Whether γ is transcendental remains unknown, a stronger unresolved question than irrationality.

• Gelfond–Schneider theoremRelated: The theorem guarantees this status for every permitted power.

• Number (mathematics)Broader topic: Transcendental numbers form a narrower class within the real and complex numbers.

• Four exponentials conjectureBroader topic: The conjecture predicts transcendence among the four exponentials.

• Mathematical constantCompared with: Transcendence separates constants such as π and e from algebraic numbers.

• Proof that π is irrationalRelated: Transcendence is stronger than irrationality, and π has both properties.