Each week I consider a different number. My books focus on maths, algorithms and computer subjects with the aim of making them accessible to as many people as possible. As well as numbers I’m also passionate about food, travel and cycling and my blog aims to widen my writing by looking at these subjects too. By identifying a number that has cropped up in my daily life during the week I then use it to take me somewhere around the globe (eg using a flight with the same number) and then I uncover a few treasures about that place. To finish with I share a simple mathematical property of the number.

I am always dreaming up travel plans and I find these blogs genuinely useful to me. At the end of the travel section I will give a conclusion about how likely I am to visit the place in question.

This week’s blog post is about the number 540. Why? Because I’ve joined a local cycling campaign and one of the worst roads in our city (Chester, England) that we must deal with is the A540. This road is about a mile away from where I live and I’d rather cycle along the pavement. The worst thing is turning right: you’re in the middle of the road with your arm pointing out and huge lorries are thundering past just inches from you. It’s terrifying.

I help with the twitter for the campaign group. Recently I tweeted what I thought was a practical observation about cycling – all about how it could improve your mental health. A cyclist tweeted right back and said that commuting along the A540 did more damage to his mental health than I could possibly imagine due to the amount of stress it caused.

Our group has campaigned to make sections of this notorious road safer as you can see here. Yesterday me and my dog walked up to the A540 to take a photograph for this post. I wanted to get one with large lorries to give a good idea of how bad it can be but the lorries weren’t in sight. However, the photograph I did manage to get does show how narrow the road is and how there isn’t really adequate room for large lorries and cyclists to travel safely along it. The traffic is travelling up to 50mph. Generally it is quite narrow for a trunk road.

So, now onto the next section. Where will the number 540 take me? Well, there is a BA540 flight between London and Bologna – wonderful! I thoroughly enjoyed doing the reading for the next section. 😊

## Bologna

I am so lucky to have been to Italy five times which shows just how much I love it. And I’d love to go back! Each trip was different. The first was a weekend in Venice, the second a week in Tuscany, the third a week on the Amalfi coast, the fourth a week in Umbria and Rome and the fifth a train trip from the border with the south of France, stopping overnight in Genoa and then on by train to Venice. The Tuscan trip and Amalfi trip were organised tours and, although enjoyable, were very much focused on the tourist-side of things. The weekend in Venice was enjoyable but too short. The other two holidays I organised myself and I particularly enjoyed these. We travelled by train on both occasions and felt perfectly free. In Umbria we stayed in what we believe had once been a monastery in Spoletto. In Rome we stayed just round the corner from the Coliseum and ate where the locals ate. For the Genoa / Venice trip we ate the best Italian food ever in Genoa (simply by asking the receptionist at our accommodation where he went to eat) – really simple food, a tiny place with huge queues outside. In Venice we stayed in a tiny flat in St Helena which was walking distance from the main sites but far enough away for us to enjoy living as the locals do with little restaurants with simple food.

Bologna has been on my radar before as the food sounds so great. I found this article and this video that reminded me of all the things I’d love to try. Obviously genuine bolognaise sauce. And I would love to try authentic lasagne and tortellini. Beef with balsamic vinegar sounds incredible too. Food tours are also a good idea – getting to taste Balsamic vinegar, exploring the markets and generally having foodie fun.

I had a look for places to stay using Vrbo (like Airbnb). I like Vrbo as it often comes up with places with character. This place which may expire is in a period building, near the city centre, under £70/night and is no bigger than we need (I object to paying for more than we’re actually going to use I feel that we’re throwing money away). There are 11 good reviews too which is reassuring. My next step would be to contact the owner and ask if it would be ok to store bikes.

I chose a week in the second half of September from a Tuesday as the summer is over here and Tuesdays often have the best priced flights. I could always investigate this further.

Cycling is good in Bologna too – not like Amsterdam – buthttps://www.tastebologna.net/blog/bike-rides-bologna bikes are catered for and it’s possible to ride around carefully. 6 scenic bike rides in and around Bologna – Taste Bologna gives a good idea.

And there’s a lot to see too. Two facts: Bologna has the oldest university of the western world and the longest portico in Italy. It’s full of towers that can be climbed. This article gives a comprehensive guide.

A little about Italy’s role in sanctions against Russia. Obviously, Italy is part of the EU but it will be affected more than other EU states by the ceasing of Russian gas as its alternatives are limited. Italy has taken in a good number of Uranian refugees who have passed through the border with Slovenia (Trieste). It’s estimate that the number could rise to 750,000 given the number of Ukrainians who already live in Italy.

Given the research that I’ve done for this post, would I go to Bologna? The answer is a definite “yes” if I was travelling through Italy by train and happened to be close – I’d be more than happy to plan my tannery to fit a few days in. I wouldn’t choose to go just to visit Bologna, however. As a place to visit I’d give it 9.5/10 (well, nothing can be completely perfect, can it?) for food, 7/10 for cycling and 8/10 for places of interest. For me to feel more inspired the cycling would need to be better.

## Abundant Numbers

540 is an abundant number. An abundant number is one for which the sum of its proper divisors is greater than the number.

The first 28 abundant numbers are:

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, and so on.

In the case of 540 its proper divisor are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270 and their sum is 1,140. As 1,140 is greater than 540, the number 540 is abundant. The amount by which the sum exceeds the number is the abundance factor – the abundance factor in this case is 1,140 – 540 = 600.

A couple of simpler examples:

The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 giving a total of 16. The number 12 has an abundance factor of 16 – 12 = 4.

The proper divisors of 24 are 1, 2, 3, 4, 6, 8, and 12, whose sum is 36. Because 36 is greater than 24, the number 24 is abundant. Its abundance factor is 36 − 24 = 12.

You may have noticed that all the abundant numbers we have shown are even. This is because the smallest odd abundant number is 945!

## Last Thoughts

Our local cycling nightmare of a road has taken me on a wonderful virtual journey to Italy where my mouth has watered whilst reading articles and watching videos about the local cuisine. Italy really is a foodie paradise and Bologna is a particularly impressive place to visit.