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, 2024	Aug. 31, 2023
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	5 years 7 months 6 days	5 years 8 months 12 days
Total, gross carrying amount	$ 67,296	$ 66,627
Definite lived intangible assets: accumulated amortization	(41,930)	(38,908)
Tradenames [Member]
Finite And Indefinite Intangible Assets [Line Items]
Indefinite lived intangible assets: gross carrying amount	$ 11,951	$ 11,939
Patents and Developed Technology [Member]
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	2 years 10 months 24 days	3 years 1 month 6 days
Definite lived intangible assets: gross carrying amount	$ 29,308	$ 28,658
Definite lived intangible assets: accumulated amortization	$ (25,460)	$ (24,402)
Customer Relationships [Member]
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	6 years 8 months 12 days	6 years 9 months 18 days
Definite lived intangible assets: gross carrying amount	$ 26,037	$ 26,030
Definite lived intangible assets: accumulated amortization	$ (16,470)	$ (14,506)