発散

• Reading: はっさん
• Romaji: hassan
• Kanji breakdown: 発 (hatsu/ha-) — emit, dispatch, send out; 散 (san/chi-) — scatter, disperse
• Pronunciation: /ha.s.sa.ɴ/

Meaning

Divergence; the spreading outward or dispersal of something, such as rays, energy, or a mathematical sequence that increases without bound. Also used to mean releasing stress or pent-up energy.

A noun (also suru-verb) with multiple senses. In mathematics, a sequence or series 発散する if it does not converge to a finite limit. In physics, 発散 describes rays spreading outward or energy dispersing into the environment. In everyday Japanese, ストレスを発散する (to release stress) is a very common informal usage. Contrasted with 収束 (convergence) in mathematical and physical contexts.

Examples

1. この級数は部分和が無限大に向かって発散するため、和は定義できない。 This series diverges because its partial sums tend toward infinity, so the sum cannot be defined.
2. レンズを通過した光は焦点距離を超えると発散し、像がぼやける。 After passing through the lens, the light diverges beyond the focal length, causing the image to blur.
3. 週末に山登りをして日頃のストレスを発散するのが彼女の習慣だ。 Her routine is to go hiking on weekends to blow off the stress that builds up during the week.

Usage Guide

Context: mathematics, physics, optics, daily life

Tone: neutral

Origin & History

Compound of 発 (hatsu — emit, dispatch) and 散 (san — scatter, disperse). Together they describe something being sent out and spreading apart in all directions.

Cultural Context

Era: Modern

Generation: All ages

Social background: Universal