Check my geometry

[Steliz]

I'm making some table mats with a geometric pattern.
First I need to mill the wood down to 15mm thickness then cut the sides at 60degs giving me a trapezoid. According to sketchup I should have a base that is 36mm and the other three sides will be 18mm (I know it says m on the sketchup model) however, having made the first angled cut and measured it I get just over 17mm which I think means I have made an error somewhere.
I thought I was good at maths but I can't see where I've gone wrong. Can anyone assist?

 

[paulrbarnard]

I can immediately see an issue with your diagram

The corner to corner length is shown as 0.53. The short edge length of one of the pieces is 0.18 and the long length of the piece is 0.36. Those two edges should add up to the 0.53.

 

[Jacob]

Assuming it is an equilateral triangle the "centre" is not in the centre.

 

[Steliz]

So it does. As it should read 54 I'm guessing this is a rounding error. I've looked in the settings for a way to add more digits but there doesn't seem to be one.

 

[Jacob]

So it does. As it should read 54 I'm guessing this is a rounding error. I've looked in the settings for a way to add more digits but there doesn't seem to be one.

Not a rounding error just not centred - given 18 the sides should be 3x18= 54

 

[Steliz]

The centre point is in the exact centre.

 

[paulrbarnard]

So it does. As it should read 54 I'm guessing this is a rounding error. I've looked in the settings for a way to add more digits but there doesn't seem to be one.

Change them all to mm. No need for extra decimal points then

 

[Fitzroy]

17mm actual vs 18mm calculated, saw kerf difference?

 

[dizjasta]

Using 15 M it is possible to get 3 positions for the triangle's centroid. Using 15.299 M the centroid of the triangular area is located accurately.

 

[J-G]

I'm making some table mats with a geometric pattern.
First I need to mill the wood down to 15mm thickness then cut the sides at 60degs giving me a trapezoid. According to sketchup I should have a base that is 36mm and the other three sides will be 18mm (I know it says m on the sketchup model) however, having made the first angled cut and measured it I get just over 17mm which I think means I have made an error somewhere.
I thought I was good at maths but I can't see where I've gone wrong. Can anyone assist?

You've mostly got things right but you are not working to a sufficiently high level of accuracy. I suspect that you are using an Metre template rather than a mm template (in SketchUp). Change that and you can work (as I do) to 6 decimal places - I'm using SU 2014 but I assume that there is a similar option in whichever version you are using, go to [Window] on the top Menu bar, then [Model Info] - [Units] from the drop-down option 'Precision' just select however many DP you wish.

If you want the Trapeziums to absolutely fit together you will need to work to a much higher tollerance than 1mm - Here is a properly scaled drawing showing that your 0.15m should in fact be 152.9978mm but you'll probably 'get away' with 153 but not 150. All the other dimensions need similar appropriate adjustment.

 

[Jacob]

I'm making some table mats with a geometric pattern.
First I need to mill the wood down to 15mm thickness then cut the sides at 60degs giving me a trapezoid. According to sketchup I should have a base that is 36mm and the other three sides will be 18mm (I know it says m on the sketchup model) however, having made the first angled cut and measured it I get just over 17mm which I think means I have made an error somewhere.
I thought I was good at maths but I can't see where I've gone wrong. Can anyone assist?

Forgot to say the obvious; if you did your drawing with pencil, ruler, compasses, it'd take minutes and be plenty accurate enough for all normal purposes.
You could choose a single dimension (length of side, height of triangle, whichever) draw it out and scale off the others. Really very simple, no calculations needed at all.

 

[Steliz]

Thanks for all the help.

Change them all to mm. No need for extra decimal points then

I looked for that setting and changed it but it didn't apply the change. I'll try opening a fresh drawing in mm and copying the triangle into it.

17mm actual vs 18mm calculated, saw kerf difference?

This will be composed of 3 different woods so I didn't factor in the kerf.

Using 15 M it is possible to get 3 positions for the triangle's centroid. Using 15.299 M the centroid of the triangular area is located accurately.

As I've already milled the wood down to 15mm that is the only measurement that is set.

J-G, thanks for the detail. I use the free web version of sketch up and the only setting I can find for units is for when opening a new drawing. I can't change the units on this one so I have copied it into another blank drawing with mm as the setting. There are no decimal places but if I scale it up by 10 I will have 4 digits and I can work it out from there.

 

[Steliz]

And here's the reworked model (with imaginary decimal place), thanks for everyones suggestions.

 

[dizjasta]

And here's the reworked model (with imaginary decimal place), thanks for everyones suggestions.

Spot on.

 

[pulleyt]

According to sketchup I should have a base that is 36mm and the other three sides will be 18mm

Apologies if this is already understood.

The trapezoid shape your after comprises three equilateral triangles as shown below. From this the relationship between the length of the long side and the short side will always be 2:1.

As Jacob indicated, this can be drawn out quite simply within a semi-circle with a known short side measurement.

• Draw a straight line and choose a centre point
• Set your compass to the trapezoid short length
• Scribe a semi-circle from the centre point
• Without adjusting the compass, use the point at which the semicircle intersects the straight line to draw an arc that intersects the semi-circle (Arcs 1 and 2.
• Join the intersections on the semi-circle to draw the required trapezoid

Just an observation, but the measurements of 18mm and 36mm make for a very small table mat

 

[J-G]

J-G, thanks for the detail. I use the free web version of sketch up and the only setting I can find for units is for when opening a new drawing. I can't change the units on this one so I have copied it into another blank drawing with mm as the setting. There are no decimal places but if I scale it up by 10 I will have 4 digits and I can work it out from there.

Hmmm...... I've just opened V2017 (I don't normally use it for a number of reasons) and although they have re-positioned the menu option [Model Info] it is still under [Windows] and the [Units] is still at the bottom of that list. I can't believe that they have removed that option in later versions - it's a fundamental 'need'.

I had mistakenly made the assumption that the 0.53m figure was your base dimension but (as has been pointed out) with 36mm as the definitive size then everything is much simpler. However the height is not 15mm it must be 15.5886mm - if you did make it 15mm you would never get the three pieces to 'fit' together.

Of course you could draw the outline using a compass/ruler and if you were making just one (maybe even 2 or 3) that might enable you to cut the pieces out by hand but if you are making a number of 'mats' then you need to set up a cutting jig of some kind -- and that does require accurate measurment.

As @pulleyt has remarked, a 54mm wide x 46.77 high triangle is a very small table mat; and (to my thinking) totally out of proportion to the 15mm thickness. Unless you are going to put 6 'sets' together to make a hexagon - which would need even better accuracy.

 

[Jacob]

.....

Of course you could draw the outline using a compass/ruler and if you were making just one (maybe even 2 or 3) that might enable you to cut the pieces out by hand but if you are making a number of 'mats' then you need to set up a cutting jig of some kind -- and that does require accurate measurment.

But doing it with Sketchup means having to round figures off so you might as well do it with a pencil to start with. Not to mention getting it wrong and going around the houses.

As @pulleyt has remarked, a 54mm wide x 46.77 high triangle is a very small table mat; and (to my thinking) totally out of proportion to the 15mm thickness. Unless you are going to put 6 'sets' together to make a hexagon - which would need even better accuracy.

It started out as 180 x 360mm but Sketchup made it too difficult.
The critical thing, and starting point, would seem to be the actual making process, which Steliz doesn't mention. On the face of it you could scale off the height from a drawing and cut/plane boards to that width (about 156mm it seems) and then mark the diagonal edges at 60º and cut, bearing in mind the kerf width. Maybe he has other ideas?

PS presumably Sketchup would have got it right if Steliz had started in mm rather than metres?

 

[Steliz]

The triangle shape will be the end grain of 3 different sticks of wood in dark walnut, light walnut and silver birch. When several slices are assembled together they produce a seemingly 3D step pattern similar to drawings by MC Escher.

Like this -

 

[pulleyt]

36mm and 18mm make perfect sense now

 

[J-G]

The triangle shape will be the end grain of 3 different sticks of wood in dark walnut, light walnut and silver birch. When several slices are assembled together they produce a seemingly 3D step pattern similar to drawings by MC Escher.

Like this -

I'll chalk that up as a good guess

It'll be easier than the last 'Escheresque' tessellation I did . . . .