Another nice example is Lehmer's number $\lambda \simeq 1.17628$, which is the largest real root of the monic irreducible polynomial $x^{10} + x^9 - x^7-x^6-x^5-x^4-x^3+x+1$. This polynomial has a second real root inside the unit circle, and the remaining roots are roots of unity.

The Mahler measure of a monic irreducible polynomial is the absolute value of the product of the roots with norm $\geq 1$. The Mahler measure of an algebraic integer is the Mahler measure of its minimal polynomial. It is believed that Lehmer's number has minimal Mahler measure. For more on Lehmer's number check out this "What is" paper.

Another nice example is Lehmer's number $\lambda \simeq 1.17628$, which is the largest real root of the monic irreducible polynomial $x^{10} + x^9 - x^7-x^6-x^5-x^4-x^3+x+1$. This polynomial has a second real root inside the unit circle, and the remaining roots lie on the unit circle.

The Mahler measure of a monic irreducible polynomial is the absolute value of the product of the roots with norm $\geq 1$. The Mahler measure of an algebraic integer is the Mahler measure of its minimal polynomial. It is believed that Lehmer's number has minimal Mahler measure. For more on Lehmer's number check out this "What is" paper.