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
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)