radices

Definition

Radices (noun, plural; singular: radix): 1. Mathematics — Base of a numeral system: In mathematics, "radices" refers to the base numbers of a positional numeral system. For example, in the decimal system, the radix is 10; in binary, the radix is 2. The plural form "radices" is used when discussing multiple bases. - Example: The radices of decimal and binary systems are 10 and 2, respectively.

  1. Mathematics — Base of a logarithm: In logarithms, "radices" denotes the base numbers of logarithmic functions. For instance, common logarithms use a radix of 10.

    • Example: Common logarithms have a radix of 10, while natural logarithms have a radix of e.

  2. Biology — Root or origin: In botany or anatomy, "radices" can refer to roots or root-like structures, such as the roots of a tooth or a plant. However, this usage is rare and technical.

    • Example: The radices of the tooth are embedded in the jawbone.
Usage Examples

  • Mathematics context:

    • The radices of the octal and hexadecimal systems are 8 and 16, respectively. (Here, "radices" refers to the base numbers of different numeral systems.)
    • In computing, understanding different radices is essential for binary and hexadecimal arithmetic. (The plural "radices" is used to discuss multiple bases.)

  • Logarithm context:

    • The radices of common and natural logarithms differ: 10 for common, e for natural. (The base numbers of logarithmic systems.)
Advanced Usage

  • "Radices of a polynomial": In advanced algebra, "radices" can refer to the roots or solutions of a polynomial equation, though this is less common and often replaced by "roots."

    • The radices of the quadratic equation were found using the formula. (The solutions or roots of the equation.)

  • Historical usage: In older texts, "radices" might be used as a synonym for "roots" in general, e.g., the radices of a tree.

    • The radices of the ancient oak spread deep into the soil. (The roots of the tree.)
Variants and Related Words

  • Radix (noun, singular): The base of a numeral system or a root.

    • The radix of the decimal system is 10. (The base number.)

  • Radical (adj): Relating to the root or origin; fundamental.

    • The radical change in policy affected all departments. (A fundamental change.)

  • Radicle (noun): A small root or root-like structure, especially in botany or anatomy.

    • The radicle of the seedling emerged first. (The embryonic root.)
Synonyms

  • Base: In mathematics, the fundamental number of a numeral system.

    • The base of binary is 2. (Synonym for radix.)

  • Root: The origin or source of something, or the solution to an equation.

    • The root of the problem is unclear. (Origin.)
Related Idioms

  • "Take root": To become established or fixed in a place or situation.

    • The new ideas took root in the community. (Became established.)

  • "Root and branch": Thoroughly or completely.

    • The organisation was reformed root and branch. (Completely overhauled.)