Now before we go on we have to remember a very simple yet very important mathematical oddity. if you have watched the Wizard of Oz you will have heard The Scarecrow say, on receiving his brain or diploma,

*the square of the hypotenuse is equal to the sum of the squares of the other two sides.*This shows symbolically how important this one little thing is and that is that in a right angle triangle, a right angled triangle being a triangle with one angle exactly 90 degrees, that if you square the length of side "A" and then add it to the square of side "B" you will get the square of side "C". It is clearer in this simplest example of this triangle the 3, 4 and 5 unit triangle where 3 x 3 or 9 plus 4 x 4 or 16 is equal to 5 x 5 or 25.

.Another way of saying this is that Side C (or 5 in our diagram) is equal to the square root of 25 - (square root simply being that number which when multiplied by itself gives us the number in question: eg. square root of 25 would be 5 ( 5 x 5) and square root of 16 would be 4 ( 4 x 4 ) and the square root of 9 would be (3 x 3 ). In any right angled triangle the small side squared plus the middle side squared

__So in the above diagram 3 would be equal to our 12 while the 4 would equal our 19 unit side. So we need to look at the image below ...__

**WILL ALWAYS EQUAL THE LONGEST SIDE SQUARED !**... and try to figure out what our "5" side is equal to. Following our formula of

**a² + b ² = c² or c = √a² + b²**So substituting in our image above we have a = 12, b = 19 and c is unknown at this time. So now all we do is substitute so we get .

**c = √a² + b² or c = √12² + 19² or c = √144+361 or c = √505 or**

__So the white line in our above diagram is equal to 22.47221 "inches". But having used certain numbers very often I immediately recognized that this number was significant for in a year on Venus there are, wait for it, there are 224.7 Earth Days, This means that Venus orbits or circles The Sun in 224.7 Earth days. I found this very nice that the length equaled the Venus Year in Earth days but could it relate to our drawing of the solar system. Well for this we have to visit NASA where it is said that Mercury is 57,909,050 kilometers on it's semi major axis (remember semi major axis is simply the average distance that a planet is away from The Sun when you take it's closest and furthest approach. Mercury being 69,816,900 km (furthest) and 46,001,200 km (closest) for a total of 115,818,100 and divided by 2 to give us 57,909,050.) Now Venus is 108,208,930. The ratio between them or the number of times Mercury's distance can divide into Venus' distance is simply 108,208,930 / 57.909.0505 and we get 1.868601367. Now since Mercury is our diagram is 12 units Venus would simply be 12 x 1.868601367 or 22.423216406. Not exactly correct but very close. Accuracy would equal 22.423216406 / 22.47221 = 99.78 % Not as close as I would like it to be but heck Tommy is only in grade 3 and I am sure he would get a passing grade. So as a recap now we have:__

**c = 22.47221 units or inches**Mercury = 12 "inches"

Venus = √505 inches

Earth = 31 inches

So now Tommy (or anyone for that matter) can draw the solar system TO SCALE by using just these three simple numbers.

We will find Mars and a whole lot more next.

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