Dual Brachistochrone curve

Dual Brachistochrone curve

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Here Is A Brachistochrone Curve That You Can Race Two Marbles From Different Points Along The Curve And See They Meet At The Bottom At The Same Time. The Tracks Are Curved, So The Marbles Should Stay Along The Middle Of The Path. The Orientation Of The Print Is Important. You Want The Grains To Point In The Direction Of The Marble'S Path (So There'S Little Resistance Along The Path From Different Points). You Can Print Another Orientation, But Sanding Will Then Be Required. I Have Yet To Print This, But I Believe The Curves Are Subtle Enough Not To Require Supports.

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Math