Online Projects

date submitted: Wednesday, July 26, 1995 4:03:08 PM

Elementary Problem of the Week

Project Coordinator: Matt Gehrett

This project is for elementary students who want to challenge their math skills and use e-mail. The problems are written by high school students. The high school students will reply to all students who submit solutions and the best answers will be posted on the internet each week.

The project can be found at http://mathforum.org/sum95/ruth/elem.pow.html

date submitted: Friday, September 29, 1995 12:17:41
PM

Project Coordinator:

I've used this project in geometry, algebra, and trigonometry. I have used it at both high school and middle school, which is where I currently teach. I got the basic idea from a professor at New Mexico Tech in Soccorro, New Mexcio. Unfortunately, I can't show a square with an exponent. Use your imagination. Adjust and adapt to your own students, and let me know the results.

Objective:  The student will be able to find Pythagorean triplets using the

formulas listed below.



PYTHAGOREAN THEOREM



A PYTHAGOREAN TRIPLET IS SQUARES WHOSE ROOTS ARE WHOLE NUMBERS.



FIRST FORMULA

"A" MUST BE ODD



A						AXA	AXA/2		B=AXA/2
-1/2						C=AXA/2 + 1/2 

3

5

7

9

11

13

15

17

19

21

23

25







				PYTHAGOREAN THEOREM



SECOND FORMULA

A= A MULTIPLE OF 4.



N	A=4N		NXN						4XNXN	B=4NXN
-1						C=4NXN + 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17







PYTHAGOREAN THEOREM KEY



A PYTHAGOREAN TRIPLET IS SQUARES WHOSE ROOTS ARE WHOLE NUMBERS.



FIRST FORMULA

"A" MUST BE ODD



A					AXA				AXA/2	B=AXA/2
-1/2						C=AXA/2 + 1/2 

3	9			4.5	4				5

5					25				12.5	12	13

7					49				24.5	24	25

9					81				40.5	40	41

11			121		60.5		60	61

13			169			84.5	84	85

15			225		112.5	112			113

17			289		144.5	144			145

19			361		180.5	180			181

21			441		220.5	220	221

23	529	264.5	264	265

25	625	312.5	312	313





			PYTHAGOREAN THEOREM KEY



SECOND FORMULA

A= A MULTIPLE OF 4.



 N
A=4N		NXN						4XNXN	B=4NXN
-1						C=4NXN + 1

1	4			1	4				3	5

2	8			4	16	15	      17

3	12				9		36	35	37

4	16	16	64	63	      65

5	20	25							100	99	101

6	24	36							144	143	145

7	28	49							196	195	197

8	32	64							256	255	257

9	36	81							324	323	325

10	40	100						400	399	401

11	44	121						484
483		     	 			485

12	48	144						576	575	577

13	52	169						676
675		      	 		677

14	56	196						784	783	785

15	60	225						900	899	901

16	64	256	1024	1023		         1025

17	68	289	1156	1155		         1157

9/26/95 at 18:40:17

From: Sharon K. Wasson

from_email: sharon_wasson@qm.kayenta.k12.az.us

project_name: Finding Pythagorean Triplets

date_of:

topic: Pre-algebra, Algebra, Geometry, Trigonometry

grade_level: 7-12

participants: 25-30 whole class

summary_of_project: PYTHAGOREAN THEOREM A PYTHAGOREAN TRIPLET IS SQUARES WHOSE ROOTS ARE WHOLE NUMBERS. FIRST FORMULA "A" MUST BE ODD A AXA AXA/2 B=AXA/2 -1/2 C=AXA/2 + 1/2 3 5 7 9 11 13 15 17 19 21 23 25 PYTHAGOREAN THEOREM SECOND FORMULA A= A MULTIPLE OF 4. N A=4N NXN 4XNXN B=4NXN-1 C=4NXN+1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 PYTHAGOREAN THEOREM KEY A PYTHAGOREAN TRIPLET IS SQUARES WHOSE ROOTS ARE WHOLE NUMBERS. FIRST FORMULA "A" MUST BE ODD A AXA AXA/2 B=AXA/2-1/2 C=AXA/2+1/2 3 9 4.5 4 5 5 25 12.5 12 13 7 49 24.5 24 25 9 81 40.5 40 41 11 121 60.5 60 61 13 169 84.5 84 85 15 225 112.5 112 113 17 289 144.5 144 145 19 361 180.5 180 181 21 441 220.5 220 221 23 529 264.5 264 265 25 625 312.5 312 313 PYTHAGOREAN THEOREM KEY SECOND FORMULA A= A MULTIPLE OF 4. N A=4N NXN 4XNXN B=4NXN-1 C=4NXN+1 1 4 1 4 3 5 2 8 4 16 15 17 3 12 9 36 35 37 4 16 16 64 63 65 5 20 25 100 99 101 6 24 36 144 143 145 7 28 49 196 195 197 8 32 64 256 255 257 9 36 81 324 323 325 10 40 100 400 399 401 11 44 121 484 483 485 12 48 144 576 575 577 13 52 169 676 675 677 14 56 196 784 783 785 15 60 225 900 899 901 16 64 256 1024 1023 1025 17 68 289 1156 1155 1157