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Patents (Details) - USD ($) | 3 Months Ended |
--- | --- | ---
Mar. 31, 2018 | Dec. 31, 2017
Finite-Lived Intangible Assets [Line Items] |  |
Patents, accumulated amortization | $ 387,550,000 | $ 382,220,000
Weighted average useful life of patents and patent rights | 4 years |
Minimum [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Useful life of patents and patent rights | 1 year |
Maximum [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Useful life of patents and patent rights | 6 years |

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