Goodwill and Other Intangible Assets (Schedule of Intangible Assets and Weighted Average Remaining Life Finite and Infinite Excluding Goodwill) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	2 years 8 months 12 days	3 years 1 month 6 days
Total, gross carrying amount	$ 54,892	$ 55,858
Definite lived intangible assets: accumulated amortization	(36,684)	(35,491)
Tradenames [Member]
Finite And Indefinite Intangible Assets [Line Items]
Indefinite lived intangible assets: gross carrying amount	$ 11,162	$ 11,312
Patents and Developed Technology [Member]
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	3 years 3 months 18 days	3 years 8 months 12 days
Definite lived intangible assets: gross carrying amount	$ 26,329	$ 27,085
Definite lived intangible assets: accumulated amortization	$ (24,106)	$ (23,931)
Customer Relationships [Member]
Finite And Indefinite Intangible Assets [Line Items]
Definite lived intangible assets: weighted average years	2 years 1 month 6 days	2 years 7 months 6 days
Definite lived intangible assets: gross carrying amount	$ 17,401	$ 17,461
Definite lived intangible assets: accumulated amortization	$ (12,578)	$ (11,560)