Trademark Geometry Usage Guide

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I'm curious on the legality of using trademarked geometry in reference to the trademark owners while not using it in the same execution. What is the legality regarding this?
Could you please clarify your location so I can provide accurate information? It's important as laws vary by jurisdiction.
This would be an international issue between the United States and Japan.
Hello ****, here are some general points to consider:
- Trademark laws differ between the U.S. and Japan.
- Under U.S. law, fair use might allow references to trademark.
- Japan has similar provisions, but interpretation may vary.
- Consent from the trademark owner reduces legal risks.
- A detailed analysis by a trademark attorney is recommended.