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Figures of fun

Chris Fautley suggests ways of making the landmarks of Hastings count

The one number irrefutably associated with Hastings is 1066. But dig deep, and you will discover more in this walk through its historic Old Town, with its opportunities to hone arithmetic and geometry skills.

Start in George Street at the entrance to the West Hill cliff railway. The railway is 500 feet long (about 152 metres), its gradient 1:3. Back in the classroom, as an exercise in scale, draw a right-angled triangle reflecting these measurements. Measure the remaining angles. Reasonably accurate draftsmen will be able to determine how high the railway climbs (about 150 feet or 46 metres). Finally, what percentage of the journey is through the 363-foot (111-metre) tunnel?

Take the railway to the top, timing the journey. Calculate average speed and ascent. Exit and enjoy the sea views. Here, you can calculate how many miles it is to the horizon. The approximate formula (for a clear day) is: 1.33 x square root of height in feet above sea level. If you are lucky, you will see the Royal Sovereign Light Tower, nine miles southwest out to sea.

How far could you see from the top of the 91-foot (28-metre) tower?

Return to George Street, walking downhill adjacent to the railway, to Hundred Steps. There are in fact 114. What percentage "extra" is this? Measure the height of one or two of them. Most are the same - eight inches (20cms). Calculate approximately how far the steps descend.

Turn left into George Street, walk to the end and turn left again into High Street. After 60 yards (55 metres), turn left into Swan Terrace; immediately to the right is St Clement's Church. Ponder symmetry by looking at the tower's south side: embedded on each side of the top window is a cannonball. Legend says only one is real - a 17th-century "gift" from the Dutch. The parishioners, put out that the symmetry of their church was ruined, installed a dummy to restore the equilibrium. Return to High Street and continue walking, noting more examples of symmetry in its numerous old buildings. On the right, No 41 is good, as is Old Hastings House at the far end, on the left. Check out the windows in particular.

Cross the main road and backtrack towards the sea via All Saints Street.

Continue until, on the left, you find a bright yellow building, the Piece of Cheese Cottage. There are no prizes for guessing its shape; suffice to say this is an ideal time to discuss triangles.

Just beyond, turn left into Crown Lane, then left into Tackleway. Walk its entire length. Many houses display the year they were built; select three, and calculate their average age. No 18, however, is dated 2001. How does this affect the average? Test mental arithmetic by adding the digits comprising the years, or multiplying individual digits together.

Return along Tackleway to its seaward end and descend Tamarisk Steps. Turn left into Rock-A-Nore Road for the East Hill Cliff Railway. With a gradient of 1:1.28, it aspires to be Britain's steepest. Repeat the earlier exercises here - the track is only 265 feet (81 metres) long, but you can walk to a height of 300 feet (91.4 metres) once on the East Hill.

The descent to sea level is via 159 steps adjacent to the railway. These lead to Tamarisk Steps, from where there are a further 60 steps to sea level at Rock-A-Nore Road. On your way down, count the number of flights then calculate the average number of steps and descent of each.

Back in Rock-A-Nore Road, seek out the Mermaid Restaurant, behind which is a building fronted with black, glazed tiles. They were used on timber-framed buildings to resemble what once were more fashionable but expensive bricks.

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