When is a trapezium not a trapezium?

Why, when it's a trapezoid of course.

There are some days when the English language is soooooo frustrating. What version should I use? Standard Australian English (SAE)? American English? British English? Living as I do in a land of many expats, from various corners of the world, I've had to learn some extra words and meanings.

Earlier this week a colleague commented to me about this topic and then e-mailed me some further information about it. The problem arose when he was teaching his students about 2-D shapes, using his personal knowledge of 50+ years, to teach them the names of various quadrilaterals. Now this learned gentleman comes from the USA, so he naturally used the US terminology, just as I would naturally use the Australian terminology. Not a problem you might say. Well, for most shapes, you are correct. There is no problem because there is no difference in the shape names. A triangle is a triangle, a square is still a square, a rectangle is definitely a rectangle (although a few might also call it an oblong), a parallelogram is still a parallelogram (or maybe it's a rhomboid), a rhombus is still a rhombus, and a kite is still a kite, no matter which side of the ocean you might be on.

But what do you call a quadrilateral with exactly one pair of parallel sides? That's where the problem comes in. If you are from the USA, then you will call it a trapezoid, but if you're an Aussie (or using an Aussie mathematics curriculum), then it is a trapezium! OK, that doesn't seem like a big issue. The problem comes in when you discover that the folk from the USA consider a trapezium to be a quadrilateral with no parallel sides. We Aussies would just call that an irregular quadrilateral!

So, I just did a search trying to find out how this anomaly came about, and found this interesting article. It seems like this problem has been around since 1795, and a resolution has yet to be determined. For those of you who like pictures, here's one I found, this one summarises the quadrilateral family quite neatly.

Oh the joys of the English language! I guess it's yet another situation where we have to think carefully about our audience, and then say, "it's not wrong, it's just different", unless you're preparing students for an exam which specifically uses one definition or the other, in which case you'd better make sure you know which one is considered correct by the examiners.

So what are we teaching our students? In the interests of consistency across the grades from K to 5, we'll call it a trapezium, but it the kids ask the question, then I'm happy to say that I will now be able to enlighten them, thanks to my learned colleague from the USA, and some Internet research.

Thinking about church

During the past day or two I've had the opportunity to read two magazines put out by the denomination of my home church. The first is a national missions magazine which you can read here, and the second is a state magazine which you can read here. The first article (on pages 6 & 7 of The QB) is written by the principal of Malyon (previously the Queensland Baptist Theological College) and looks at the issue of church attendance. This was very interesting and I was able relate to a number of points which he made.

When I was growing up, church on Sunday mornings was basically not negotiable. It was what you did. It wasn't a chore, it was an important part of being a committed Christian. We also attended Sunday School which was usually before the service. To the best of my recollections Sunday School went for an hour, then there was a short break (maybe half an hour) and then we went to church. The whole family attended the whole service together (except for babies & toddlers who went to nursery / creche). Services rarely went longer than an hour, unless there was communion, in which case it might go for an extra 15 minutes. Up to the end of primary school we were allowed to read a book during the sermon (or colour in when we were smaller) but after that we were expected to listen to the sermon. The rest of the service we were expected to join in with. Consequently I grew up learning many hymns. When I reached my teens, Scripture Choruses were becoming popular and so the music began changing. Over the years I've seen so much change in church services. Some of those changes I enjoy, but others I find a struggle. I distinctly remember that once we went into the sanctuary we were required to be quiet. Usually the organ would be playing quietly for 5-10 minutes before the service started and people took time to be quiet and prepare for worship. That's something I really miss.

Getting back to the article, the focus was on the changing regularity of attendance. It was noted that many folk often attend fortnightly (every two weeks) these days, and that is even stretching out to every third week. The writer reflects on a number of reasons for this changing attendance trend, varying from the busyness of our lives, through to pure laziness and rebellion. I know that for me personally I find it hard to attend every week, and I sometimes wonder if attending church on Saturday instead of Sunday would be a good option for me. One of the reasons for that is that I find I'm really ready for a "down day" or "Sabbath" on Saturday, and Sunday is the day when I'm more productive in preparing for the week ahead. Unfortunately teaching is not the 8 - 5 job that I had for the first 20+ years of my working life. When you work in a job which doesn't require additional hours of planning, preparation, and marking, it's somewhat easier to be committed to attending church every Sunday. Regardless of whether I'm attending every Sunday or not, it's important to have a local church where I feel connected, both to the Lord in worship and to fellow believers.

The other article (on pages 8 & 9 of Resonate) talks about the purpose of church, discussing churches as being selling or sending churches. Selling churches are about delivering goods (meeting the needs of the members of the congregation), while sending churches are about equipping members to reach out to the community. I think there needs to be a balance of both. It's important to meet the spiritual needs of the congregation, to encourage and build them up so that they can effectively reach out and serve. What do you think?