Three mountains steeped in mythology and legend

A historic Highland peak

A conical mountain of striking elegance that stands in the very heart of northern Scotland, Schiehallion is richer in "history and mystery" than any other Highland peak, said Oliver Smith in the FT. In folklore, it features as a fairy realm, the site of a magical well, the haunt of a witch with "frosted hair", and so on – tales perhaps rooted in some more ancient animistic belief. And thanks to its simple form and its isolation, it was chosen in 1773 by Charles Mason (he of the Mason-Dixon Line in the American colonies) for use in the first successful attempt to work out the mass of the Earth. Overseen by the astronomer royal, Nevil Maskelyne, the experiment involved calculating the mountain's mass (a job for which Charles Hutton pioneered the use of contour lines) and observing the relative strength of its gravitational pull (using a pendulum) – after which the rest was a matter of deduction. More recently, Schiehallion has given its name to a brand of lager, a folk band, and an investment fund, while a lovely hotel – the Fortingall – has appeared beside it, making a great base for the relatively easy hike to its 1,083m summit.

Gods and monsters in northern Greece

An isolated massif with numerous peaks in northern Greece, Mount Olympus was held by the ancients to be the seat of the gods. Today, "history and mythology lurk everywhere" around its flanks, and at 16 miles across, it offers plenty of divinely beautiful hiking, said Mike Unwin in The Times. I spent two days exploring it with a guide during a self-drive trip around the region with the tour operator Sunvil. The week began in the lively city of Thessaloniki, and included a visit to Aigai, the capital of ancient Macedon, where I saw "dazzling" frescoes, a hoard of golden artefacts and the remains of the palace where Alexander the Great was crowned. On Olympus, only "serious" climbers can reach the summit – Mytikas, Greece's highest peak, at 2,918 metres; I hiked instead to the nearby peak of Skolio, which is a fraction lower. The long walk down through wild country, home to wolves and golden eagles, was wonderful. I also visited nearby sites rich in legend such as the "stunning" Orlias waterfall, where the river supposedly vanished underground after refusing to purify the Maenads who murdered Orpheus. The trip costs from £2,092pp for seven nights, including flights and private guides (sunvil.co.uk).

A sacred summit in Washington state

Rising above Seattle "like a deity holding the city in judgement", Mount Rainier is one of the tallest peaks in the contiguous US, said Jacqui Agate in Wanderlust, and the most topographically prominent too. Long sacred to the region's indigenous peoples (some of whom know it as Tahoma), it has for more than a century been surrounded by its own national park. Its summit is best left to serious climbers, but its lower slopes make fine hiking. Rich in Douglas firs, western hemlocks and western red cedar, the old-growth forest here is marvellously lush. Some of the cedars are 1,000 years old, and their "broad canopies" explode like "emerald fireworks". In early spring, I had to wear snow shoes for the hike up to Myrtle Falls, which tumbles 18 metres and has Rainier's summit as a backdrop. I combined my visit with trips to two of the other glorious wild places in Washington state – the Olympic National Park (with its "flower-embroidered" meadows and "skyscraping" peaks), and the San Juan Islands, where the orca-watching is among the best in the world.

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