An 85-year-long Harvard study found that positive relationships are the single biggest contributor to happiness, with friendships playing a central role. According to the research, maintaining stable, long-term friendships is one of the seven habits associated with happier and healthier lives.However, not all friendships serve the same purpose. As reported by CNBC, the ancient Greek philosopher Aristotle identified three distinct types of friendships, and Arthur Brooks, a Harvard professor who teaches a course on happiness, believes all three are essential for a fulfilling life.The three types of friendshipsIn his article, The Best Friends Can Do Nothing for You, which is featured in the Harvard happiness course, Brooks outlines Aristotle's three categories of friendship.Utility friendshipsThese relationships are built around practical benefits and shared goals."Think about the relationships you have with people with whom you work, or with whom you do business. These relationships tend to be transactional in nature," wrote Brooks.Friendships based on pleasureThese friendships are rooted in shared interests and the enjoyment people derive from one another."This type of relationship is based on mutual admiration because each person draws pleasure from the other. If a person finds their friend funny, interesting, and a source of enjoyment, it is likely a friendship of pleasure," Brooks wrote in his article."Perfect" friendshipsAccording to Aristotle, the deepest and most meaningful friendships are those built on mutual care and a shared commitment to something greater than personal gain."By Aristotle’s standards, perfect friendships are those between people who have a mutual love for something that not only brings them together, but elevates their behavior to virtue. A relationship is perfect not when it is based on utility or pleasure, but when it is focused on improving the circumstance of the other person," Brooks notes.Why all three matterAs CNBC explains, utility friendships may not always be deeply satisfying, while friendships based on pleasure can remain limited to shared hobbies or interests. Even so, Brooks argues that both types are valuable because they help people navigate different aspects of life.These relationships are useful for advancing in life, "but they don’t usually bring lasting joy and comfort," Brooks wrote.He also notes that while utility and pleasure friendships have their place, they often lack the depth needed for vulnerability and honest conversations.While we need utility and pleasure friendships, "we can’t afford to risk these connections through confrontation, difficult conversations, or intimacy," says Brooks.For that reason, Brooks believes "perfect" friendships are indispensable for lasting happiness."You might not be able to put it into words, but you probably know how these ‘perfect’ friendships feel," Brooks wrote. "They often feature a shared love for something outside either of you, whether that thing be transcendental (like religion) or just fun (like baseball), but they don’t depend on work, or money, or ambition."