Curious about right angles, Sian Prior takes a trigonometric journey to forest and ocean in the state's south-west.
A bloke I know has a passion for visiting geographical right angles. Show him a map of Australia and he'll show you a cornucopia of corners. From the coast to the inland, from Cape Howe to the Surveyor-General's Corner, he's visited them all.
It always seemed slightly bizarre to me, until I began planning my first trip to the south-west of Western Australia.
Staring at the squashed-lamington shape of the Australian mainland, I have a sudden inkling of how satisfying it might be to explore that snug corner between Albany and Perth.
Dusting off my trigonometry skills, I decide the best approach to this isosceles triangle would be to fly the length of the hypotenuse from Perth to Albany, then dawdle west towards the Cape Leeuwin corner before heading north to Perth. After all, what could possibly be more satisfying than visiting a corner where two oceans - the Indian and the Southern - meet?
Our tour begins with a few days in the south coast town of Denmark, which, according to a local travel brochure, is ''equidistant from the towns of Walpole, Albany and Mount Barker''. Equidistance - already they're speaking my language. My partner and I have arranged to stay in a friend's house. Perched above the shores of Wilson Inlet, the house has been built to blend with the landscape.
No right angles here; even the wooden deck curves around a giant granite boulder.
Beyond the boulder is a stand of karri trees. It's my first sighting of these legendary tall eucalypts of the south-west and, as we sip cocktails on the deck, I admire the way their pale trunks reach unwaveringly towards the sky.
Ten minutes' drive from Denmark, Ocean Beach curves southwards from the Wilson Inlet entrance, nestling in the protective arm of Wilson Head. The swell is strong, though, and the lifesavers keep the gap between the flags absurdly narrow.
Surfers, boogie-boarders and bodysurfers duck nimbly out of each other's paths as we all scramble for the best wave in the set.
Afternoons are spent at the dazzling rock pools dotted along William Bay, 15 minutes' drive west of Denmark. Greens Pool is so perfectly proportioned, it looks like the creation of an overexcited resort developer. Shaped like a three-cornered flag, this natural sea pool is bordered by the beach on one side, a huge stone slab on another and a string of jagged rocks at the top, protecting swimmers from the crashing waves.
There's a fissure at the top left-hand corner of the triangle, where a current of water called the shute pours through a rock-lined passageway and into the pool. Donning snorkels and goggles, we jump in and watch fish and stingrays dart out of our way as we hurtle towards the calm oasis of turquoise seawater.
Just east of Greens Pool is Elephant Rocks, where, with a little imagination, you can believe you've stumbled upon a herd of grey giants snoozing in the shallow water.
Around the gentle curve of the next point we find Madfish Bay, a rectangular version of Greens Pool - perfect for swimming laps. The eponymous fish don't make an appearance but a few mad fishermen stand on the ocean edge of the rock wall, ducking the spray.
Our final day is spent on the vast body of water encircling the historic port city of Albany. The plan is to sail a small yacht from Princess Royal Yacht Club through King George Sound and around the corner into Oyster Harbour. Our captain is a retired family doctor with a deep tan and the cabin walls are covered in miniature triangles - winner's pendants from his yacht-racing triumphs. Today, though, the pace is leisurely as he guides us around the harbour, pointing out the ruins of the Old Forts Lighthouse keeper's house on rocky Kings Point.
Leaving Denmark and heading west, our next destination is only 50 kilometres away in Nornalup National Park. Turning north off the South Coast Highway at Bow Bridge, we head deep into the shady eucalypt forest, following the signs to the Valley of the Giants Tree Top Walk.
The valley is home to a stand of 400-year-old red tingle trees, up to 70 metres high. These relics of the super-continent, Gondwana, grow only in a region of about 1000 hectares and, in spite of their sturdy appearance, they're vulnerable to people tramping on their root systems. So in the mid-1990s, a series of six bridge spans was constructed above 40-metre pylons, creating a fractured hexagonal walkway that zigzags for 600 metres through the treetops.
Wandering among the swaying tips of those giant tingles, I experience the same out-of-body exhilaration as when I first snorkelled above a coral reef; the realisation that there is another world here and it's not one designed for humans. The bridges are built to sway slightly, too, so I'm glad to reach the corners where two spans meet on small platforms above the pylons.
As dusk falls we cruise westwards and spend the night at the Pemberton Hotel. Once a logging town, Pemberton is now enjoying a steady flow of travellers keen to explore the nearby karri forests. Just behind the town, in Gloucester National Park, is the highest fire lookout tree in the world. At more than 60 metres, the Gloucester Tree is a daunting prospect for vertiginous visitors, even with wire netting partially enclosing the spiral ladder. Imagine the courage required from the original fire scouts who began climbing those 153 metal spikes in the 1940s without protection and in all weather.
By the time we drive to Augusta, a whipping wind has overtaken us and it's spitting with rain. The weather is a reminder of how exposed this corner of the state is to the immense, colliding forces of nature. We drive slowly past the grey waters of Hardy Inlet towards Cape Leeuwin, the south-western-most tip of the continent.
If on the map this corner of the state resembles an overfed hammerhead shark, then the Cape Leeuwin Lighthouse is its left eye, swivelling east and west and blinking as it overlooks the Southern and Indian oceans. Standing at the foot of the stippled stone tower, I gaze at the roiling water, hoping for some visual marker of the subaquatic corner where the two oceans connect.
But any sailor knows there are no right angles once you leave land. Instead I conjure an image of the Antarctic Circumpolar Current swirling eastwards, cooling the Southern Ocean like a dash of chilled spirits in a cocktail, countering the tropical warmth of the Indian Ocean as the two vast bodies of water mingle below the white caps.
I think back to that wonky wooden deck in Denmark, shaping itself to the curve of the warm boulder. The 3D messiness of nature will always be more satisfying than any two-dimensional lines we might draw on a map.
Qantas flies to Perth from Melbourne for about $228 (4hr) and from Sydney for about $260 (5hr 15 min). Virgin Blue, Jetstar and Tiger Airways (Melbourne only) also fly to Perth. Skywest Airlines flies from Perth to Albany for about $160 (75 min). Fares are one way including tax.
Valley of the Giants Tree Top Walk, on the South Coast Highway between Walpole and Denmark, is open daily 9am-5pm. Adults $10, children $6, families $25. See www.valleyofthegiants.com.au.
The Gloucester Tree is a 10-minute drive from Pemberton. Day pass for a car is $10. See www.australiannationalparks.com/westernaustralia/Gloucester.
Cape Leeuwin Lighthouse is a 10-minute drive from Augusta. Adults $5, children $3. Guided tours, including entry fee, cost adults $15, children $7. See www.margaretriver.com/pages/cape-leeuwin-lighthouse.
Staying and eating there
The Pemberton Hotel, at 66 Brockman Street, Pemberton, has family rooms from $170 a night. See www.pembertonhotel.com.au.
Sweet tooths should visit Dark Side Chocolates, 10 Hollings Road, Denmark, for hand-crafted treats made by winemaker-turned-chocolatier John Wade.
Pick your own punnets of strawberries, raspberries, loganberries, boysenberries and marionberries in December and January at Denmark Berry Farm, 61 Lantkze Road, Denmark. See www.denmarkwa.asn.au/operators/BerryFarm.htm.
For an excellent pub meal in Albany, visit the 1865 Earl of Spencer Inn. See www.earlofspencer.com.au.