MAW-joo-luus
/ˈmɔdʒulʊs/
modulus is pronounced MAW-joo-luus (/ˈmɔdʒulʊs/). Modulus refers to the absolute value of a real number, or more generally to a measure of size or magnitude in mathematics and engineering. In engineering contexts it often denotes the modulus (or absolute value) operator, while in geometry it can denote the flexible parameter describing a circle’s circumference relative to its diameter. The term is used across disciplines to indicate a nonnegative magnitude, irrespective of sign.
Modulus refers to the absolute value of a real number, or more generally to a measure of size or magnitude in mathematics and engineering. In engineering contexts it often denotes the modulus (or absolute value) operator, while in geometry it can denote the flexible parameter describing a circle’s circumference relative to its diameter. The term is used across disciplines to indicate a nonnegative magnitude, irrespective of sign.
"The modulus of −7 is 7 in the real-number system."
"In mechanics, the modulus of elasticity relates stress to strain."
"Compute the modulus of the complex number z = a + bi."
Pronounce it as MOH-duh-luhs for US/UK/AU, with primary stress on the first syllable. IPA: US/UK: /ˈmɒ.djʊ.ləs/ or /ˈmɒ.dʊ.ləs/ (varies by speaker); AU tends to /ˈmɒ.djʊ.ləs/ or /ˈmɒ.dʌ.ləs/. The middle syllable often reduces to a schwa, so it sounds like mod-ju-lus with a light, neutral vowel. Ensure the final -lus is a clear, unstressed syllable. Audio reference: listen for the crisp initial consonant cluster and the soft middle vowel.
Common errors: (1) Misplacing stress as MO-dyo-lus instead of MOH-duh-luhs; (2) Inserting a long 'u' sound in the second syllable as /ˈmɒdjuː.ləs/ rather than /ˈdʒu/ sound; (3) Final '-lus' pronounced as /ləs/ with a strong 's' rather than a light, unstressed schwa–like ending. Correction: keep the middle as a short mid vowel with a light /ləs/ ending. Practice with slow enunciation: /ˈmɒ.djə.ləs/; ensure the 'dj' cluster is distinct but not prolonged.
In US English, the first syllable tends to be /ˈmɒd-/, with a more rounded /ɒ/ and a lighter /ɪ/ or /ə/ in the second syllable. UK English often keeps /ˈmɒ.djuː.ləs/ or /ˈmɒ.djʊ.ləs/ with a slightly more rounded second vowel; AU often mirrors UK but may reduce the middle vowel to /ə/ and reduce final to /ləs/ or /ləs/. The main differences lie in rhotics and vowel quality: US tends to be rhotic, UK less so in non-rhotic accents, and AU typically aligns with non-rhotic British pronunciation in casual speech but may show Australian vowel shifts.
It’s challenging due to the consonant cluster in the middle (/dj/), the short mid vowel in the second syllable, and the final -lus with a subtle /ləs/ vs /ləs/ variation. Speakers often misplace stress, over-articulate the middle vowel, or lengthen the final syllable. To master it, practice a clean onset on syllable 1, a quick but subdued middle vowel, and a softly unstressed final -lus, aiming for /ˈmɒ.djə.ləs/.
A unique aspect is the potential pronunciation variation of the middle vowel: /ɪ/ as in 'bit' vs. /ə/ as in 'sofa' can appear depending on speaker and context, but in technical speech the middle vowel often reduces to a schwa. Paying attention to the transition from the /d/ to /j/ helps avoid 'mud-julus' or 'mod-ju-lus' mispronunciations. The correct sequence emphasizes /d/ followed by a soft /j/.
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The word modulus comes from Late Latin modulus, meaning ‘measure, standard, rule’, from Latin modulus ‘small measure, standard of measure’, from modus ‘measure, bound, limit’. In Latin, modus carried the sense of a boundary or limit in arithmetic, proportion, or proportionate ratio. In mathematical usage, modulus later specialized to denote a measure of magnitude; in geometry and mechanics, it appears in terms such as modulus of elasticity and modulus function. English adoption traces to 17th–19th century mathematical treatises, where scholars used modulus to denote a fixed measure, a standard of comparison, or a bound. The modern general sense of the absolute value of a number evolved as mathematics formalized the modulus operator, emphasizing nonnegative magnitude. The term’s first known uses appear in classical and early modern mathematical texts, where “modulus” described a standard of measurement and a bound, and later extended to signal the magnitude of complex quantities and vector norms. Over time, modulus gained specialized meanings in optics, material science, and number theory, but maintaining the core sense of a nonnegative size or distance from zero.
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Words that rhyme with "modulus"
-lus sounds
-cus sounds
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