Last Blog Entry

Hello,

Since my last blog entry I've been investigating a couple question that I've asked myself and other had asked me.

"Is there any other side lengths, of a right triangle, that are not triples?"

My answer to this is simple. No. There isn't any other whole numbers that can create a 90 degree triangle without it being a decimal. For example, in my previous blog the right angle stayed the same but as i changed some numbers it became clear that all of the side length would have to change also.



As i was messing around with the numbers to see if i can find any close right triangle that isn't a triple, three numbers seem to pop up in my face. The way i came up with those three number was by thinking that, if i were to add one to the triples would that give me another right triangle? hm mm' These particular number were 8-9-12 (estimated from 12.042). although it had made a triangle with a angle that was 89.602, it seems very close to a right triangle. I have tried to see if there was more i can be able to depict out of this theorem.

I know they might be some question about whether or not there is more "triples" that seem close to right trianglesm but i will make sure to get more one that.

Blog 4

"What would happen if you changed one side and kept the angles the same? How would the hypotenuse change? What original questions do you have about right triangles?"

The Hypotenuse "BC" had changed but not by to much. I had tried this investigation with the triangle triple, 3-4-5. I had kept 3 the same and the angle was 90 degrees. The difference between the changes of the Hypotenuse was not much, but it changed about 1.0. For example,

AB	AC	Hypotenuse	Angle	Differents between AC and BC
4	3	5	90
4	4	5.657	90	0.657
4	5	6.403	90	0.746
4	6	7.211	90	0.808
4	7	8.062	90	0.851
4	8	8.944	90	0.905
4	9	9.849	90	0.925
4	10	10.774	90	0.925
4	11	11.705	90	0.931
4	12	12.649	90	0.944

What i had found out is that if you were to change one side by 2 then the difference would be 2 but if u change it by just 1 the difference would also be 1. One question that i have about right triangles is, Is there any other side lengths, of a right triangle, that are not triples?

Blog 3

"If you take a right triangle, and change one side length, how does that change the other the other side lengths? How does that change the angles of the triangle?"
I had taking one right angle that had the side length AB=3.0, AC=4.0, and BC=5.0. I decided to switch side length AC to 7.0 and the result of that came out very strange. Although i had changed one of the side length the rest just stayed the same number but the angles changed. The right triangle i once had was now a obtuse triangle.

As if that was enough investigating i tried more thing to find behind the scenes. For example,

		Stays The Same	Change to Liking	Change due to AC	Difference
		AB=3	AC	BC
		3	4	5
		AB=3	AC=6	6.708	1.708
		AB=3	AC=8	8.544	1.836
		AB=3	AC=10	10.44	1.896
		AB=3	AC=12	12.369	1.929
		AB=3	AC=14	14.318	1.949
		AB=3	AC=16	16.279	1.961
		AB=3	AC=18	18.248	1.969
		AB=3	AC=20		1.976

The difference between these small changes is what came out to be my answer. The answer is (about) 2.0 overall.

Blog 2

Since my last entry, i have investigated two questions, "could I add the new triple to itself and get another triple? Is there any other operation I could do on a triple to get another triple?"
If i were to add a new triple to itself, i would get another triple . For example,

• 5-12-13 added to itself gives...
• 10-24-26 added to itself gives...
• 20-48-52 added to itself gives...
• 40-96-104 added to itself gives...
• 80-192-208 added to itself gives...

There seem to be no proper limit to my equation.

Any operation that involves multiplying all three number by the same digit well end up as another triple. For example,

• 3-4-5 multiplied by 4...
• 12-16-20 multiplied by 3...
• 36-48-60

Pythagorean triples are right triangles that have integer side lengths. How many of these are there? Can you predict when they will occur?

I know that 3-4-5 are Pythagorean triples but when you add 3 to it self, 4 to itself, and 5 to itself you get another triple 6-8-10. I had to make sure I was right so I had done it to the rest of the triples and it shows I was correct. I came up with a equation that seem to work for all of the basic triples. This equation has to be applied to all three number to find more triples and know when they occur. For example, 5-12-13. My equation is 2n, and if you apply this to the 5-12-13 triplet you will get another triplet which is 10-24-26.