We hear about "falling standards", exams getting easier. In my youth, 1 in 12 pupils got to go to university. Now it's 1 in 3.

Is todays' generation really that more clever?

I remember about 3 years ago a UK broadsheet published questions from different Exam standards. The first was from a first year Uni exam (geometry) asking to work out angles on a 2d triangle. (stuff I remember from my 3rd year Grammar)

The second was a hypothetical question about same 2d triangle and a student defined internal 3d triangle. The question came from a Chinese Uni entry exam.

Is the West falling behind in Academia?.

Here's a question from a few years ago.

Given 2 parallel and equilateral triangles with the area between them divided into 3 equally shaped trapezoids, compute the area between the two triangles as the sum of the areas of the 3 trapezoids. The equilateral triangle sides are 60 and 10.

Easy, right? Knock yourselves out. A surprise for the correct answer.

I was going to post the question in general......then I though....naa. Anybody who hasn't posted 500 times on this site is much too smart. More fun to tax the few remaining brain cells in Bedlam.

Regards.

Well, I've just helped my daughter with her chemistry homework, so I'm shot for the day.

Well, I've just helped my daughter with her chemistry homework, so I'm shot for the day.

In Thai ?

OP:

Anyway, of course there are many more students and also on a much tougher workload of study than in the past, due to so many reasons but a few are:

* many parents are 'richer' now than in the past and thus able to afford to send their kids to uni's

* the world/country population grew enormously; in 1950 the world had a ''mere'' 2.5 Billion; now we have 6.7 Billion.

* Nutrition (don't shoot me!) and thus body and brains are fed better

* science itself became more diverse and developed with the speed of light in the past 5 to 6 decades; diseases of which humans still died 50 years ago can now be cured.

But, to discuss "Intelligence" or if the human race is getting more intelligent.... is asking for WWIII

http://en.wikipedia.org/wiki/Intelligence

LaoPo

We hear about "falling standards", exams getting easier. In my youth, 1 in 12 pupils got to go to university. Now it's 1 in 3.

Is todays' generation really that more clever?

I remember about 3 years ago a UK broadsheet published questions from different Exam standards. The first was from a first year Uni exam (geometry) asking to work out angles on a 2d triangle. (stuff I remember from my 3rd year Grammar)

The second was a hypothetical question about same 2d triangle and a student defined internal 3d triangle. The question came from a Chinese Uni entry exam.

Is the West falling behind in Academia?.

Here's a question from a few years ago.

Given 2 parallel and equilateral triangles with the area between them divided into 3 equally shaped trapezoids, compute the area between the two triangles as the sum of the areas of the 3 trapezoids. The equilateral triangle sides are 60 and 10.

Easy, right? Knock yourselves out. A surprise for the correct answer.

I was going to post the question in general......then I though....naa. Anybody who hasn't posted 500 times on this site is much too smart. More fun to tax the few remaining brain cells in Bedlam.

Regards.

I don't understand the question because it doesn't have all the information that I need (perhaps I'm a case in point of lagging in intelligence!). Parallel triangles? Do both apices (sp? apexes?) point in the same direction or diametrically opposite, or towards each other? ie. do they both point upwards, one up and one down, or apex to apex. Is the base of them 10 or 60? What is the distance between them...are they touching at one point? 3 trapezoids....isn't the area between the triangles also triangular, one or 2 triangles if they are touching or one trapezium if they are not touching? 3 equal trapeziums as a regular shape equals one larger trapezium, ie the shape of the space between the triangle if they do not touch each other and are both pointing in the same direction.... ... we need to know what is the distance between the triangles, assuming that both bases are on the same plane and both apices point in the same direction and there is no point of contact (ie giving a trapezium between them).

If the shape of the inbetween area is a trapezium, why break it down further into three trapezoids?

We are still monkeys, we just have better toys than sticks.

We hear about "falling standards", exams getting easier. In my youth, 1 in 12 pupils got to go to university. Now it's 1 in 3.

Is todays' generation really that more clever?

I remember about 3 years ago a UK broadsheet published questions from different Exam standards. The first was from a first year Uni exam (geometry) asking to work out angles on a 2d triangle. (stuff I remember from my 3rd year Grammar)

The second was a hypothetical question about same 2d triangle and a student defined internal 3d triangle. The question came from a Chinese Uni entry exam.

Is the West falling behind in Academia?.

Here's a question from a few years ago.

Given 2 parallel and equilateral triangles with the area between them divided into 3 equally shaped trapezoids, compute the area between the two triangles as the sum of the areas of the 3 trapezoids. The equilateral triangle sides are 60 and 10.

Easy, right? Knock yourselves out. A surprise for the correct answer.

I was going to post the question in general......then I though....naa. Anybody who hasn't posted 500 times on this site is much too smart. More fun to tax the few remaining brain cells in Bedlam.

Regards.

I believe we're looking at a parallelogram as the ultimate shape of the two triangle, three trapezoid placements. Don't have time to play around with it now but . . .

I do seem to notice the extraordinary emphasis placed on intelligence by so many. Throughout my readings regarding the economic crisis I've so often heard many calls for the need of "smart" people to be our "leaders." Well, gosh, we have a lot of very smart people as leaders now. Unfortunately, they're using their smarts to satisfy their own ends.

I read once somewhere that if the universe had to rely solely on intelligence to uphold it's workings that intelligence alone would not be able to keep the earth in it's orbit for a nanosecond. I see intelligence as merely one of our attributes as humans. I view intelligence as more or less a tool. It can be used for many things but ultimately it needs to have a direction. What provides the direction?

I've also read somewhere that ideally intelligence needs to be blended with our other attributes in order for us to produce a well functioning society as a whole. If intelligence were to be overly relied upon it is simply not up to task and the result of that over reliance would be the creation of problems for ourselves. I look around in the world and see plenty of problems. Is that what the world is lacking? Higher intelligence by a greater portion of the population? Personally, I highly doubt it.

We hear about "falling standards", exams getting easier. In my youth, 1 in 12 pupils got to go to university. Now it's 1 in 3.

no way that this ratio is correct.

We hear about "falling standards", exams getting easier. In my youth, 1 in 12 pupils got to go to university. Now it's 1 in 3.

no way that this ratio is correct.

In America the ratio is greater than 2 in 3 moving on to some kind of post secondary education. I'm not sure what kinds of colleges that number comprises, nor do I know how many complete their studies.

I don't understand the question because it doesn't have all the information that I need (perhaps I'm a case in point of lagging in intelligence!). Parallel triangles? Do both apices (sp? apexes?) point in the same direction or diametrically opposite, or towards each other? ie. do they both point upwards, one up and one down, or apex to apex. Is the base of them 10 or 60? What is the distance between them...are they touching at one point? 3 trapezoids....isn't the area between the triangles also triangular, one or 2 triangles if they are touching or one trapezium if they are not touching? 3 equal trapeziums as a regular shape equals one larger trapezium, ie the shape of the space between the triangle if they do not touch each other and are both pointing in the same direction.... ... we need to know what is the distance between the triangles, assuming that both bases are on the same plane and both apices point in the same direction and there is no point of contact (ie giving a trapezium between them).

If the shape of the inbetween area is a trapezium, why break it down further into three trapezoids?

Maybe you missed the "equilateral" bit. I.e., all sides are of equal value. (1st triangle 60, 2nd triangle 10) Also their angles would be the same, 60 degrees. Therefore there would be no up or down. For 2 equilateral triangles to be in parallel, (sides) they would have face the same way, up, down, or whatever you choose. Parallel triangles tend not to touch. Hope that helps.

Regards.

Harcourt.

Please accept my apologies for the smugness of my previous post.

Personally, I was lost after trapezium.

The point I should have made was that the question came from a Sumerian school tablet, dated 1900BC.

Hmmm Uploading the file is not allowed.

Can be viewed here.

http://www.earth-history.com/Sumer/Clay-tablets.htm

My question still stands. People (the elite no doubt) were studying modern Uni level geometry.....4000 years ago.

Regards.

Ok, I'll 'fess up. I've never even heard of a parallel triangle. Hope the kids don't drag any of that kind of homework home.

Harcourt.

Please accept my apologies for the smugness of my previous post.

Personally, I was lost after trapezium.

The point I should have made was that the question came from a Sumerian school tablet, dated 1900BC.

Hmmm Uploading the file is not allowed.

Can be viewed here.

http://www.earth-history.com/Sumer/Clay-tablets.htm

My question still stands. People (the elite no doubt) were studying modern Uni level geometry.....4000 years ago.

Regards.

No apology needed, I didn't get one iota of smugness....you were right, I overlooked "equilateral", read "60 and 10" and assumed isoceles.

I still don't see 3 trapezoids in the space between the triangles, not equal ones anyway.

Your point about education 4000 years ago is as nteresting as the problem.

There is a PC trend in some schools to make sure all students "achieve", the so called dumbing down. Dumbing down can be as outrageous as "widening the goal posts", ie making the pass mark so low that most anybody can pass, or it can be as silly as awarding every student an award as if mere participation was enough.

4000 years ago it would have been the elite that studied and I would bet that the studen's mandate was to learn the subject to know it instead of today's attitude of cramming enough to pass an exam.

If you extend the lines (sides) of the inner triangle, to touch the sides of the outer triangle, either clockwise, or anticlockwise, (not mixed) it will form 3 trapeziums.

Regards.

If you extend the lines (sides) of the inner triangle, to touch the sides of the outer triangle, either clockwise, or anticlockwise, (not mixed) it will form 3 trapeziums.

Regards.

Ahhhh....one is within the other. I see now. Thanks.

Well that's just high school geometry. I don't have a high education (High school and a couple of years tertiary) but I see that it's not that difficult.....but what IS amazing is to solve it without Pythagoras, 4000 years ago. I don't think Pythagoras was around that far back.

I would only know how to solve it using Pythagoras' Theorum.

err okay so what they want is the area of each trapezoid or the area of the big triangle less the smaller one?

On topic, embarrassingly I was listening the Chris Moyles podcast and one of the crew sat a GCSE paper on geography and scored an A.

He got 57% correct...

Excellent Silva. Cut to the chase of the question in one short phrase.

In my "O" level days, 57% was an E/F. 49/45% being the basic "O".

Still no answers though.

The answer lies in H. Height....the distance between the parallel lines. Take trigonometry (300BC) an a protractor (1800 AD) out of your toolbox and the problem is slightly more than High school level.

In fact, using the tools of the day, ( A compass ((dividers)) and a straight-edge) just posing the question is a task in itself.

Can your kids draw an equilateral triangle with a compass and a straight edge?

I personally find Harcourts "dumbing down" statement to be rather profound.

One of the arts of maths is number crunching.The human mind finds links and tunnels between sets of numbers. Computers just crunch numbers.

Regards.

What parallel lines? I did spherical trig regularly as part of my occupation and I still never heard of a parallel triangle. It's almost an oxymoron.

Lanna,

The question states 2 parallel triangles. I.e. 2 triangles with sides parallel to each other. 1 Parallel triangle, is, as you stated, an impossibility. So we have 2 equilateral triangles, (60 an 10) the smaller one obviously inside the bigger one and equidistant. (parallel)

As Silva so succinctly put it....."Find the difference in area between the little triangle an the big one".

Was 1900 BC the origins of legalease??

Regards.

Oooh, uh, OK. Now I have a headache. Maybe tomorrow, or uh, maybe not.

Keep up with the Dylan lyrics.....love "em.

Regards

Keep up with the Dylan lyrics.....love "em.

Regards

Thanks. I always got more out of Dylan than say, The Bible.

Unfortunately this has too many characters for a signature:

Come senators, congressmen

Please heed the call

Don't stand in the doorway

Don't block up the hall

For he that gets hurt

Will be he who has stalled

There's a battle outside

And it is ragin'.

It'll soon shake your windows

And rattle your walls

For the times they are a-changin'.

The last 3 lines does it for me.

Regards.

Come off it! Drawing an equilateral triangle using a compass and straight edge is one of the most basic things in geometry.....my high school years were 30 years ago and I can still remember.

Draw a line x units in length, scribe arcs x units diameter centred on each end of the line, and where the arcs intersect is the third point of your equilateral triangle. I would hope my 13 year old could do it....but sadly I suspect he would have to be prompted because the kids are not taught critical thinking skills....skills that encourage the kids to use what they know in ways that are different from the specifics that they have been taught.

It's solving the problem without Pythagoras that has me stumped. As mentioned above, it's the difference between the big and the little triangles;

Bisect the (60 unit) equilateral triangle and you have 2 right angle triangles of hight z, base 30, and hypotenuse 60. Using "the square on the hypotenuse equals the sum of the squares on the other two sides", h² = z² + 30², or z² = 60² - 30² = 3600 - 900 = 2700.

Root 2700 = 51.96

Area of a right triangle is 1/2base * hight, in this case 15 * 51.96 = 779 square units.

So the area of the 60 equilateral triangle is 2 * 779 = 1558 square units.

Do the same for the 10 unit triangle, subtract from the larger...and you have it.

But without Pythagoras (circa 2500 years ago) I'm at a loss at first glance.....and perhaps also after some thought too . You're right TeleT, the answer lies in the distance H between the two triangles.....but I suspect that it too is fairly simple geometry achievable with just a straight edge, a compass, and some number crunching..... if you know what to do.

Surely this is an example of "specialised knowledge" not greater intelligence or education.

Your'e all talking <deleted>. It was definately Burt Lancaster and he was the only one to achieve a Triple Somersault

On another note (which is incidentally back on topic) Can anyone name some recent major life changing inventions ? I really can't think of many inventions lately that have transformed or had a huge impact on our lives. I'm not talking about going from 1gb memory sticks to 32gb, they are just improvements to an invention. I'm talking about the likes of the home Computer, the light bulb, telephone, electricity etc.

Passing exams isn't really a good indication as to whether or not we are getting more intelligent. That could be just people are just getting better at learning things, parrot fashion.

I do seem to notice the extraordinary emphasis placed on intelligence by so many. Throughout my readings regarding the economic crisis I've so often heard many calls for the need of "smart" people to be our "leaders." Well, gosh, we have a lot of very smart people as leaders now. Unfortunately, they're using their smarts to satisfy their own ends.

I read once somewhere that if the universe had to rely solely on intelligence to uphold it's workings that intelligence alone would not be able to keep the earth in it's orbit for a nanosecond. I see intelligence as merely one of our attributes as humans. I view intelligence as more or less a tool. It can be used for many things but ultimately it needs to have a direction. What provides the direction?

I've also read somewhere that ideally intelligence needs to be blended with our other attributes in order for us to produce a well functioning society as a whole. If intelligence were to be overly relied upon it is simply not up to task and the result of that over reliance would be the creation of problems for ourselves. I look around in the world and see plenty of problems. Is that what the world is lacking? Higher intelligence by a greater portion of the population? Personally, I highly doubt it.

Any takers?

I do seem to notice the extraordinary emphasis placed on intelligence by so many. Throughout my readings regarding the economic crisis I've so often heard many calls for the need of "smart" people to be our "leaders." Well, gosh, we have a lot of very smart people as leaders now. Unfortunately, they're using their smarts to satisfy their own ends.

I read once somewhere that if the universe had to rely solely on intelligence to uphold it's workings that intelligence alone would not be able to keep the earth in it's orbit for a nanosecond. I see intelligence as merely one of our attributes as humans. I view intelligence as more or less a tool. It can be used for many things but ultimately it needs to have a direction. What provides the direction?

I've also read somewhere that ideally intelligence needs to be blended with our other attributes in order for us to produce a well functioning society as a whole. If intelligence were to be overly relied upon it is simply not up to task and the result of that over reliance would be the creation of problems for ourselves. I look around in the world and see plenty of problems. Is that what the world is lacking? Higher intelligence by a greater portion of the population? Personally, I highly doubt it.

Any takers?

Greater intelligence would ultimately be able to cross any hurdles that cropped up by shere force of brilliance.

Having said that, I think intelligence tempered with the so-called EQ, or emotional intelligence would be a be a better recipe for success.

The hindrance to the human race growing more intelligent is that we interfere with evolution with our morals, ethics, and laws.

Humans rose above mere animals because of greater intelligence. We are physically weaker than other animals, especially apex predators......but we are smarter, and thus managed to outwit those that would eat us to extinction, or outsurvived them through detrimental environmental factors.

If left to our own devices, we may have evolved into a race of geniuses......but we weren't smart enough to see the future. A future full of degenerates and idiots, pissing in the gene pool, slowing down the rate at which genius can rise to the top.

Eugenics!!!!

Your'e all talking <deleted>. It was definately Burt Lancaster and he was the only one to achieve a Triple Somersault

On another note (which is incidentally back on topic) Can anyone name some recent major life changing inventions ? I really can't think of many inventions lately that have transformed or had a huge impact on our lives. I'm not talking about going from 1gb memory sticks to 32gb, they are just improvements to an invention. I'm talking about the likes of the home Computer, the light bulb, telephone, electricity etc.

Passing exams isn't really a good indication as to whether or not we are getting more intelligent. That could be just people are just getting better at learning things, parrot fashion.

I agree. Competition and the desire to succeed above others has led to a culture of "get that piece of paper that says you are good" (an acedemic certificate) even if it means not actually learning the subject. Students are taught to pass, not taught to learn.

Love ya cellphone?

I consider the, the most dangerous invention since guns and ammo.

Think about it...........