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From its zenith on the great Beartooth Plateau in the Absaroka-Beartooth Wilderness all the way down to a heartbreakingly beautiful U-shaped valley bounded by granite peaks, that river imprinted itself on the hearts of Montanans who fished it, hunted its headwaters and walked beside it on the famous Beaten Path.

Instead, expedition guide and certified geology nut Stephanie Gallo made me appreciate the wonders of Dawes tidewater glacier tucked in a U-shaped valley at the head of Endicott Arm, its gorgeous blue color the result of compressed layers deforming due to the weight of overlying snow and ice, the short, blue light wavelengths transmitted and scattered.

With its massive walls of granite towering toward the sky and waterfalls that plunge into a U-shaped valley filled with giant sequoias and incense cedars, Yosemite is among country’s most visited parks, drawing 4 million people a year.

“This is the Big Boy,” Mr. Clarke said, pointing to a 10-foot-tall half-pipe — imagine a U-shaped valley upon which a skater can propel himself back and forth, gaining momentum and height — that was the centerpiece of the park when it opened.

Lao Huang’s house was a low-slung shelter of stone surrounded by gardens and tea fields that extended deep into the gentle slope of a U-shaped valley.