When we were in school, geometry was an irritating business perplexingly attacked with scratched plastic protractor, triangles, murderous dividers and compass. It was baffling right from the start, when we learned that the thing called a set square was, in fact, triangle-shaped.
I never imagined that one day I'd be thrilled to the bones by the subject. But a trip last month to northern Italy and to some of its angular, green gardens convinced me that geometry, applied with precision, grace and grandeur, is one of the most satisfying, exciting and delightful things in the world.
At Villa Barbarigo at Valsanzibio, not far from Padua, the 17th-century garden is announced by a magnificently pompous portico, sitting with typical Italian nonchalance at a bend in a country road. The massive Portal of Diana, lavishly pillared, arched and garnished with muscular statues, is presided over by the huntress and her dogs. Down below in a huge pond, scurries of gold fish paint the water with fast orange brushstrokes.
This was once the grand entrance to the property, but now visitors (of the paying variety) come in a modest gate further down and are immediately plotted onto a fascinating grid delineated by high box hedges, hornbeam allees and a broad, pleated ribbon of water made up of stepped fish-ponds. Fountains and lichen-covered statues mark almost every interstice and each line of vision terminates in a pleasing picture: an ornate gate, the bosky Euganian Hills or the perfectly symmetrical villa - a worn patchwork of peach, pink and flesh-coloured render.
The intense heat is magnified by the catty odour of box hedging and the high-pitched electric tone of a cicada rising periodically over the non-stop, rhythmic thrumming of unknown insects. Relief comes when we are drenched by the giochi d'acqua or water jokes, jets of water that are automatically triggered when we approach some inviting stone benches.
More entertainment is to be had in the boxwood maze, one-and-a-half kilometres of narrow paths tightly coiled into a neat square. I take the spoilsport's direct route to the central mount, but my husband takes the inquisitive, manly route. Even with me directing operations from above, he gets hopelessly and hotly ensnarled.
Valsanzibio is a slightly dusty treasure quietly ageing in a fold in the Euganian Hills. It is the country cousin of the opulent villas which encrust either side of the Brenta canal, the waterway between Padua and Venice. Here - just a few hours by gondola - wealthy Venetians escaped the crowds of the city each summer.
THE 18th-century, 114-room Villa Pisani was built for an influential banking family which included Alvise Pisani, who eventually became the Doge of Venice. The 10-hectare grounds, laid out by architect Girolamo Frigimelica in 1720 in the then-popular French style, are beautifully conserved and in a continual state of restoration. It's heartening to see avenues of ancient lime, chestnut and plane augmented with new, recently planted trees, ensuring the geometric framework will continue to be as strong as the day it was conceived.
Surprisingly, one of the most awesome, linear features in the gardens, a wide canal shooting from house to Palladian-style stables, was added in 1911. But it's thoroughly in keeping with the rest of the park which is systematically divided and redivided by a precise network of rides and paths. The design is emphasised again and again by strategically-placed heroic statues, temples, arches and a neatly square little "coffee house" on a mount. There's a maze here too, in seemingly tip-top condition, but during our visit it is closed for maintenance. A delightful citrus garden where lemons, limes and oranges grow in huge pots heavily mulched with manure is hidden away behind a thick hornbeam hedge.
Villa Pisani was chosen by Mussolini as a rendezvous for his first historic encounter with Hitler in 1934. They met in a silk-clad corner room under a painted ceiling decorated with lyres. On that day, the villa and its grounds must have teemed with self-important militia, and the marble halls must have rung with their steel-tipped heels. On the day we visit, the place is disturbed only by a small band of soft-shod tourists and dainty, darting lizards.
Garden reading: Penelope Hobhouse's Gardens of Italy (Mitchell Beazley, £14.99 in UK) is an excellent guide to over 100 gardens. It's invaluable if you are planning a visit.
Back at home: Bantry House in west Cork is one of several Italian-inspired gardens in Ireland. Nigel Everett has just published An Irish Arcadia, on the making of Bantry's gardens during the last century. The 63-page, illustrated booklet makes edifying reading for students of garden design and history. Available from Mr Everett at Borlin, Bantry, Co Cork, it costs £5.95 including postage - proceeds go to the Chernobyl fund and the children's oncology unit at Mercy Hospital.