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, 2023	Aug. 31, 2022
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	5 years 8 months 12 days	2 years 8 months 12 days
Total, gross carrying amount	$ 66,627	$ 54,892
Definite lived intangible assets: accumulated amortization	(38,908)	(36,684)
Tradenames [Member]
Finite And Indefinite Intangible Assets [Line Items]
Indefinite lived intangible assets: gross carrying amount	$ 11,939	$ 11,162
Patents and Developed Technology [Member]
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	3 years 1 month 6 days	3 years 3 months 18 days
Definite lived intangible assets: gross carrying amount	$ 28,658	$ 26,329
Definite lived intangible assets: accumulated amortization	$ (24,402)	$ (24,106)
Customer Relationships [Member]
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	6 years 9 months 18 days	2 years 1 month 6 days
Definite lived intangible assets: gross carrying amount	$ 26,030	$ 17,401
Definite lived intangible assets: accumulated amortization	$ (14,506)	$ (12,578)