General aviation pilot reported a near miss with a helicopter while entering the traffic pattern at a non-towered airport. The pilot did not follow normal published traffic pattern entry procedures and created the traffic conflict; then landed normally.

Narrative

I was released from my IFR flight plan for a visual approach and was told to squawk VFR and change frequency. I made position calls beginning at about 10 miles south of the airport. I heard there was a helicopter using Runway 16. I announced that I was descending from 4;000 ft and was 10 miles from the airport and will enter left downwind for Runway 16. The helicopter was making good position calls; but I was never able to find him. It wasn't until I was very near the airport that I realized I was lining up for Runway 03 instead of Runway 16 and that my 45-degree entry intention was skinny. I realized I was over the departure end of Runway 16; still a little high for pattern altitude; so I immediately turned wide for the downwind on the real Runway 16. I landed normally and didn't see the helicopter (he was on right downwind for RWY 16 at this time) until I turned base for Runway 16. The helicopter pilot gave me his phone number for me to text him so he could call me after he landed; which he did. He said we came too close was he was on the upwind for Runaway 16 and that I should never cross over the departure end while entering a pattern. I explained my error and I discussed what I should have done better. After being released from IFR; I should have swung wider to enter left downwind for RWY 16 on a more accurate 45-degree angle. Even with the error I made today in mistaking RWY 03 for RWY 16; if my entry angle to the pattern were better; I would not have crossed over the departure end of RWY 16 as I had done mistakenly.