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Goodwill and Other Intangible Assets (Schedule of Intangible Assets and Weighted Average Remaining Life Finite and Infinite Excluding Goodwill) (Details) - USD ($) $ in Thousands | Aug. 31, 2025 | Aug. 31, 2024
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Finite And Indefinite Intangible Assets [Line Items] |  |
Definite lived intangible assets: weighted average years | 5 years 6 months | 5 years 7 months 6 days
Total, gross carrying amount | $ 67,694 | $ 67,296
Definite lived intangible assets: accumulated amortization | (44,363) | (41,930)
Tradenames [Member] |  |
Finite And Indefinite Intangible Assets [Line Items] |  |
Indefinite lived intangible assets: gross carrying amount | $ 11,997 | $ 11,951
Patents and Developed Technology [Member] |  |
Finite And Indefinite Intangible Assets [Line Items] |  |
Definite lived intangible assets: weighted average years | 2 years 6 months | 2 years 10 months 24 days
Definite lived intangible assets: gross carrying amount | $ 29,641 | $ 29,308
Definite lived intangible assets: accumulated amortization | $ (26,545) | $ (25,460)
Customer Relationships [Member] |  |
Finite And Indefinite Intangible Assets [Line Items] |  |
Definite lived intangible assets: weighted average years | 6 years 7 months 6 days | 6 years 8 months 12 days
Definite lived intangible assets: gross carrying amount | $ 26,056 | $ 26,037
Definite lived intangible assets: accumulated amortization | $ (17,818) | $ (16,470)

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