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, 2021	Aug. 31, 2020
Finite And Indefinite Intangible Assets [Line Items]
Amortizable intangible assets: weighted average years	3 years 1 month 6 days	3 years 6 months
Total, gross carrying amount	$ 55,858	$ 57,368
Amortizable intangible assets: accumulated amortization	(35,491)	(33,891)
Tradenames [Member]
Finite And Indefinite Intangible Assets [Line Items]
Unamortizable intangible assets: gross carrying amount	$ 11,312	$ 12,321
Patents and Developed Technology [Member]
Finite And Indefinite Intangible Assets [Line Items]
Amortizable intangible assets: weighted average years	3 years 8 months 12 days	4 years 3 months 18 days
Amortizable intangible assets: gross carrying amount	$ 27,085	$ 27,082
Amortizable intangible assets: accumulated amortization	$ (23,931)	$ (22,905)
Customer Relationships [Member]
Finite And Indefinite Intangible Assets [Line Items]
Amortizable intangible assets: weighted average years	2 years 7 months 6 days	3 years 1 month 6 days
Amortizable intangible assets: gross carrying amount	$ 17,461	$ 17,965
Amortizable intangible assets: accumulated amortization	$ (11,560)	$ (10,986)