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Stay away from the person. Avoid eye contact. Communicate through others. Curtail your responses. Tune out negative behavior. Find strengths in numbers, if necessary.
Avoidance is sometimes the easiest way to ignore someone. If someone is getting on your nerves, try to keep your distance as much as you can.  You can avoid places they're likely to hang out. If an annoying co-worker always eats lunch at noon, try eating lunch outside of the office or taking a later lunch. Avoid social situations where you're likely to see that person. If annoying person from school is going to be at party this weekend, try making other plans. When you're in the same room with someone who annoys you, be aware of your eyes. If you accidentally glance at the person, this could result in eye contact. This can be misinterpreted as an invitation to come over and talk. When you're around the person, try not to look at them. This will help minimize interactions. If you work with someone, you sometimes have to communicate with them. It may be easiest to do it through others. You don't have to be rude about this. Do not, for example, say within the person's earshot something like, "Could you tell Jeff, who I'm not speaking to, to put his dirty dish in the sink?" You can, however, ask others to deliver information when necessary. For example, you're working in a group for a work project. The annoying person is in your group. You may ask one of your group members to talk to the person, or you might only reach out to them via email or text message. You can't completely avoid talking to someone, especially if you see them at work or school. You don't want to give a complete silent treatment when someone's talking to you, so work on curtailing your responses. When someone talks, give curt responses like "Hmmm" and "Okay." This will hopefully send the message that you want some space. If someone is pessimistic or highly critical of things, try to ignore it. Ignoring it may help you stay positive without their negativity affecting you.  For example, if your office mate constantly complains about how much work they have, try ignoring them so that you don't feel bad about your own work. You shouldn't ignore everything. If a co-worker always teases you to the point you feel uncomfortable around them, confront them. You can say, "Would you mind not joking about my outfit? I enjoy what I wear, but it makes me feel bad when others criticize how I dress." If the annoying person is very aggressive towards you, adopt the buddy system. Try to have friends or co-workers accompany you places you're likely to see the person. Friends can, for example, walk with you between classes or eat lunch with you to keep the annoying person away.